CIP / 005 ISBN 7-30-08496-X Ⅰ Ⅱ Ⅲ - - Ⅳ G634 603 CIP 004 353 ISBN 7-30-08496-X/G 380 0087 http / /cbs pku edu cn 67505 58874083 67656 xxjs@pup pku edu cn 675490 787 09 6 4 75 383 005 005 9 00
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003
6 獉獉獉 獉獉獉獉 999 Ⅰ
Ⅱ
0- CD OB EF OA 3 4 AOB 5 0- AOB = 3 AOB + = AOB + 4 = 80 AOB = + - + - + + + - - - + - - - + EF OA 0- AOB = 3 AOB + = 80 AOB = CD OB AOB = 3 CD OB AOB + = 80 CD OB AOB = 0- CD OB AOB 3 AOB 4 AOB 0-3 40 6 0-3 6 6 0- Ⅲ
45 988 3 a b c x a < b < c x - a + x - b + x - c Ⅳ
- x - a - x - b - x - c x a x - a - x - b - x - c a < x b = x - a + x - b - x - c b < x c x - a + x - b + x - c x > c a + b + c - 3x x a - a + b + c - x a < x b = - a - b + c + x b < x c 3x - a + b + c x > c Ⅰ x a a + b + c x a a + b + c - 3a = b + c - a Ⅱ a < x b - a + b + c x b - a + b + c - b = c - a Ⅲ b < x c - a - b + c x x x > b - a - b + c + b = c - a Ⅳ x > c - a - b - c x x x > c 3c - a + b + c - c - a - b Ⅰ Ⅱ Ⅲ Ⅳ a < b < c c - a < c - a + b - a = b + c - a c - a < c - a + c - b = c - a - b Ⅱ c - a x = b - 3x + a + b + c x a - x - a + b + c a < x b = x - a - b + c b < x c 3x - a + b + c x > c f x = x - a + x - b + x - c 0-4 f x x = b x = b f x f b = b - a + b - b + b - c = c - a 0-4 0-4 Ⅴ
0-5 x - a x a x - a + x - b + x - c x a b c 0-5 x = b a c a - c = c - a 0-6 0-6 a < b < c < d x b c b c 0-6 d - a + c - b a < b < c < d < e x = c e - a + d - b a b c d x a b c d x 4 989 4 989 990 99 99 Ⅵ 987 6 3 a 槡 b = 槡 a 槡 b a b 0 a b 0 槡 a b = 槡 a 槡 b a 0 b > 0 槡 ab = ab 槡 a 槡 b = 槡 a 槡 b = ab 槡 ab 0 槡 a 槡 b 0, 槡 ab = 槡 a 槡 b a 0 b > 0 a ( b ) 槡 ( ) = a b 槡 a 槡 b = 槡 a 槡 b = a b a 槡 b 0 槡 a 槡 b 0 a, 槡 b = 槡 a 槡 b a 0 b > 0 a a 槡槡 b = b a 槡 b = 槡 b b = 槡 a 槡 b 槡 b 槡 b
M log a N = log am - log a N M N a > 0 a x = log a M N y = log am z = log a N a x = M N a y = M a z = N a x = a y a = a y - z z x = y - z log a M N = log am - log a N M N a > 0 a log a M N = log a M N + log an - log a N = log a M N N - log an = log a M - log a N 988 989 4 990 99 5 P 987 4 k = R k = 0 R 0-7 0-7 Ⅶ
獉獉 ΔΦ k = lim Δ s 0 Δ S 3 0-8 MN MN 0-8 989 99 99 3 4 5 Ⅷ
a b c x a < b < c x - a + x - b + x - c 3 0-9 ABCD AD BC AB DC E EG AC EH BD G A D H GA= DH GC HB EG AC 0-9, S ACG = S ACE S DBH = S DBE S ABC = S DCB S ACE = S ABC + S BCE S DBE = S DCB + S BCE, S ACE = S DBE, S ACG = S DBH AD BC, C B GADH h S ACG = GA h S DBH = DH h GA= DH BC EG EH M N AM DN 0-0 ACMG DBNH S ACMG = S ACM S DBNH = S BDH AC = AC EG AC, S ACM = S ACE S BDN = S DBE S ACE = S DBE S ACE = S DBE, S ACMG = S DBNH 0-0 Ⅸ
AD BC, ACMG DBNH GA DH h S ACMG = GA h S DBNH = DH h GA= DH S ACE = S DBE S ACE = S DBE GC HB ACE DBE S ACG = S DBH GA = DH S ACMG = S DBNH GA= DH E EG EH M N G H a 3-8a + 7 = a 3 - a - 7a + 7 = a a - - 7 a - = a - a + a - 7 = a 3-8a + 8 - = a 3 - - 8 a - = a - a + a - 7 = 8a 3-7a 3-8a + 7 = 8a 3-8a - 7a 3-7 = 8a a + a - - 7 a - a + a - = a - a + a - 7 7 - + 8 a 3-7a 3 + 8a 3 a = a 3 - a + a - 8a + 7 = a a - + a - a - 7 = a - a + a - 7 x - a + x - b + x - c a < b < c a < b < c < d a < b < c < d Ⅹ
0- BO CO ABC ACB MON BC MN = BM + CN MON BC, = 3 =, = 3, MO = BM NO = CN, MN = MO + NO = BM + CN 0- CO BO ACB ABC MNO BC MN = BM - CN MNO BC, = 3 =, = 3, MO = BM NO = CN, MN = MO - NO = BM - CN 0-0- BMO CNO + + 3 + + 99 + 00 = + 00 + + 99 + 3 + 98 + + 50 + 5 = 0 50 = 5050 + + 3 + + 99 + 00 50 5 0-3 Ⅺ
x - a + x - b + x - c n n 3n 0-4 0-3 0-4 3n n n n n n 3n Ⅰ n n n k n 3n - k n n Ⅱ < n n l l n - l k l + n - l = n + l l Ⅱ n n n n Ⅰ 3n n Ⅱ n n Ⅰ Ⅱ Ⅻ
! 3 5 8 a b a + b b + a 5 + 3 = 3 + 5 3 a + b = b + a 3 4 a + b a + b a + b a b a + b a b a + b a b a + b a b a + b a b a + b a b
a + b h S = a + b h a + b h S = a + b h > < > <
" 3 獉獉 獉獉獉獉 0 - - a a - a a - a a - a - a 0 a a a a a > a a a = a a a < a a a = a a a > a 0 a 獉獉獉獉 a a a = { a a 0 - a a < 0 3
{ a a > 0 a = 0 a = 0 - a a < 0 a = 0 a = 0 a > a = a a = 0 a = 0 0 = - a a a > 0 a = { - a a 0 a = - a a < 0 a - b b - a a b P P x - a + x - b + x - c a - b a b 3 - - - 3 4 3 4 6 + 3 = 6 + 6 3 6 + 3 6 + 6 3 + 3 6 = 6 + 3 6-6 + - 6-6 - = - 6 = - 7 5 ( ) 3 3 5 5 3 3 4 = 5 = 7 8 7 3 8 9 8 7 3 = 8
9 3 4 35 4 35 + 35 4 786 3 786 3-5 0-0 5 0 0 + 5 3 6 3 3 0 0-5 0 0 + 5-0 5 { } { - 5 0 3 6 } { - 5 0 } { 3 0 + 5 3 6 } { - 5 0-0 } 3-0 5 0 0 + 5 5-0 5 - - ( - 0 5 ) 5
- 3-0 5 0 0 + 4 5-6 7-5 - 8-6 7-6 7 = 6 7 = 36 4-5 6 36 4 > 35 4, - 6 7 < - 5 6 = 5 6 = 35 4-8 = 8 = 8 00 = 7 5 = 49 75-7 49 75 < 50 75, - 8 > 7 = 7 = 50 75 獉獉 5 獉 3 ( ) - 40 4 + 09 44-0 5 3 4 4 3-4 3 - - = - 8 89 44-0 5 3 4 4 3-4 3 = - 8 89 44-4 3 4 3-0 = 89 4-4 3 4 4 3-4 3 3 h h 4 h h - 4 3 3 4 0 - - 3 Ⅰ - - - - = 0-40 4 + 09 44 4 3 ( ) - 0 5 3 4 4 3 40 6
Ⅱ = - 89 h h 5 ( 4 + 09 44 ) - h 4 3h 4 3h - 0 = 9 5 ( 4 + 09 44 ) 6 4 = 9 5 4 09 6 + 9 6 = 80 + 09 = 89 44 a b a b c a + b + c = 0 a b + b c + c a b c c a a b c a b c 0 a b c 0 a a > 0 a = { - a a < 0 a a > 0 = a { - a < 0 b b = b > 0 c { - b < 0 c = c > 0 { - c < 0 a + b + c = 0 a b c a b c a >0 b <0 c a >0 b >0 c <0 a b c 0 a a > 0 a = { - a a < 0 b b = b b = a a = a a = { - b < 0 b > 0 { - a < 0 a > 0 c c = c c = { - c < 0 c > 0 a + b + c = 0 a b c a b c a + b + c = 0 a > 0 b < 0 c < 0 a > 0 b > 0 c < 0 a > 0 b < 0 c < 0 = - + - - + - = - a > 0 b > 0 c < 0 = + - + - = - a b c 0 a b c 7
3 a a > 0 = a { - a < 0 a + b = 0 a b A B C D a b = 0 a b A C B 3 a + b = 0 a b D A B C D 4 a 3 + b 3 = 0 a b A B C D 5 a b = 0 a b A B C D 6 x < - - + x A + x B - - x C x D - x 7 A B C D b 8 a = b a = 9 b a < b < a 0 a - a 3 50 > 5 x + 4 x - x - x + 8 5-3
6 7 8 9 ab < 0 a + b b - a 0 a + b = a + b a b 0 0000 a > a a 3 a a - a 7-875 8 66-3 3 6-5 0 65 + 3 8 6-6 4 5 < 0 5 5 - - - 4 3 0-4 - 4 6 7 8 9-5 6-5 7-874 - 7 8-8 - 7 9-5 - 3-5 + - 3-5 - 3-5 - 3 30 a - a 3 - a a 3 a a 33 a + b a + b 34 a - b a - b 35 a b a b 36 a a 37 x y x y 38 x = y = 3 x + y 39 - + - 3 + 3-9 5 {[ ( 8 ) + 3-0 5 ] - 4-6 } ( - 3 ) - 0 75 5 ( - 5 ) 40 - + - 4-3 5 4 9
( 5 ) ( 8 ) ( ) 3 [ - - 5 ] 4-5 43 7 95-7 44 9 875-45 47 8-0 5-3 8 ( ) ( ) 0 5-4 3 3 ( ) 3 [ + ] 3 3 6 7-7 + 4-3 - 3-5 + 3 5 3 5-46 - 3-3 3 ( ) 3 + 0 5 - - 0-6 + 4 4 3 m + n 48 m n - m + n 4-0
# = > < - 3a b 7-3 7 a x - y x - y a x - y - 3a x - y - a x - x = - 3 6 - x 6-3 x = 3 x 6 - - 3 a = 3 4 b = - 5 6a b 4-5 - 5 6 a 6 3 獉獉
- 5 6y - 3y + - 5y - 6-3 - 0y y = - 3 a = 3 b = - 6 a - b 3-3a - b 5 3 = - 30y + 5y - 5-30y - - 3 + 30y = 5y - 8-30y + = - 5y + 4 y = - 3 a = 3 b = - 6-5 - 3 + 4 = 49 a - b 3-3a - b = 3 - - 3 [ ( 6 ) ] - 3 ( ) 3 = ( ) - 3 = - 8 7 8 ( ) [ - - 3 6 ] = = - 5 6y - 3y + - 3-0y 5y - 6 y - 5y - - 6-6 y - - 6 5y - y + 6 5y - y - - 30y + 3x - x - 5 x - x - x 3 - x - x - x - = 3x - x - 5 x - 3x - 6x - x - x - x - = 3x - x - 5 x - 3x + 6x - x + x - x - = 3x - x - 5 5x - x - = 3x - x - 5x - x + = 3x - - 5x + = 3x + 50x - = 50x + 3x -
3 3 a - b - c + d = a - b - c - d = a - b + - c + d = - - a + b + - c + d = - - a + b - c - d + + - - + 3 x = - x - x + A 3 B - 5 C - D 7 a = 3 4 b = - 7 a + ab + 7 A 3 B 6 7 C 67 3 ab - b A a C ab 4 x 5-6xy + y 3 y B 0 D 6 D A 5 B 3 C D 0 5 6m - 5 m - 6 + m - m - 6 A m - m - 4 B m + 4m + 4 C m - m + 4 D m - m - 4 6 x x a bc a + b - 0 5a x - 7 x 3y 3 ab 5 8 ab a 9 x 4 y + x 3 y + x y 3 x 0 a 3-6a b - ab + a b b 3
- x 4 + 5x 3-6x - 5x + 7x 4-6x y - 3xy 3 + x 3 y y 3-5a 3-6b + 7ab - 4a b 3 4 + 4 - x - - x - 6 7-5 x - x + - - + 6x - x 5-5 5 5ab - a - 7b - 6a - ab - - 4 4a - ab a = 4 3 b = - 6 3x + 5x - 5x - x + 4 4
$ x y z 5 - a - = 4 + a a - x + = x + + x x x x + = x + + x x - = 0 x - = 0 獉獉獉 x = x = 5
Ⅰ a = + a = + a = - a 3 = - a 4 m = + a + a m = m Ⅱ n = - a - a 3 4 n n Ⅰ Ⅱ x - x = x = - x - 0 0 - x + 6
x 3 5 - x - = - x = 5-5x - = - x = 3-5x = - x = - 5x + x = - 3 3 = - 4x = - 4 = x = 4 5 5 5 4 4 80 4 5 7
x x = 4x + 5-80 80 80 = 4x + 5 - x 3 4 4x = x + 80-5 4 5 5 = x + 80-4x 5 x = 4x + 5-80 6 4x + 5-80 = x 7 4 4 x + 80-5 4 = x 8 x + 80 = 4x + 5 9 x 80-5 4 - = x 9 3 9 8 9 4 5 6 7 A B x A B B A B 9 A B x 8
5 6 7 B A B 8 4 5-6x = 3 8 - x - 4 + x = 6 - x - - 5-6 x = - 8-6x - 8 - x = 6 - x + - 5-8x = - x - 8x + x = - 7x = x - 7 x = - 7 x = x = - 3 4 ax = b a 0 5 x = b a 3 9
( ) [ ] x - 6-6 3 5 x + = 3 7 x - 5 x + 5 - x - 6 = 5 0 35 x - + 3 5 x + = 3 7 x - 35x + x + 35 = 5x 56x - 5x = - 35 x = - 35 4 0 x + 5 - x - = 60 0x + 50 - x + = 60 9x = 9 x = - 0 x + 0 - x - = 5 0 x + 0 5 x + 5 x + 5 0 x + 5 5 x + 0 x + 5 - x - 3 7x - - 0 x = 0 04 0 08-5x + 0 0 4-0 x 0 6 3 - x - = 4-0 8 0 03 0 x - 0 0 0 7x - 4 = - 0 x 3-5x + 0 00 6 0
5x 0 4-0 x 0 8 0 8 4-0 x 40 - x 4-0 x 3 4-0 x 0 8 8 8 0 6 3 - x 0 0 6 3 - x 0 0 03 6 30 - x 3 0 x - 0 0 0 x 0 0 0 0 0x - 0 0 4 3 4-0 x - 0x - 0 = 4-30 - x 4 38 0 6 : 3: 4 3 36 x x x x - 38 38 0 = 0 x x x - 38 x - 38-0 + x = x + 0 - x + 6 x = 3 3-38 = 6
x x 3x 4x ( ) x + 3x + 4x - = 36 3 x = = 4 3 = 36 4 = 48 x x + 38 x x a x - x x x - x + 5 5 35 30 4-4- 30 x x - 30 35 x - 30-5 x - 30 = 35x 35-5 x - 30 = 35x x = 35 x - 30-5 x - 30 35 35 35 = 35x + 5 x - 30 x - 30
3 = = = 6 8 630 0 8 8 8 0 3 8 39 360 = = 3 = ( 3 ) + + = x x 8x + 0 + 8 = 630 8 + 3 0 x + 39 x - = 8 630 3
- 7 0% 50% 800 0% 0 40% 3 0% 00 5% 30% = = = - = + = = - = = x 800 - x 0% + x = 800 50% - 0% 800 - x = - 50% 800 x 0 0% = 0 - x 40% 0-0% - x = 0 - x - 40% 3 x 00 - x x 5% + 00 - x 30% = 00 0% x - 5% + 00 - x - 30% = 00-0% - 4 4 A B C D
A B C D 3 A B C D 4 A B C D 5-5 - - 5 6-4 6x - 5 7 - x = x + 8-4 6-4 - 5 7 - - 4 = - 4 + 8-4 - 5 = 4-79 - 4, - 4 6x - 5 7 - x = x + 8 7 x - x - 6-0 3x = x - 4 8 9 0 5 - x - x = 5x 8 - - x 5 5-0 x - x - 0 = 4 0 0 - x + 0 x = 0 004 + x 0 0-0 06x + 0 5 ( ) [ ] 6-8 + x = x + 5 7 5 7 - x + 0 3 - - x 5 = 4 4 5 3 40% 70 50% 05 4 5 5 7 5 5 8 3 7 0 6 400 A 8 0 A 5
% x y x = a y = b x = a { y = b x = a y = b x = a y = b a x + b y = c a x + b y = c a b a b a a = b = c = b c a b c a b = c = 0 a x + b y = c a x + b y = c a b a b a = b c a b c 3 a x + b y = c a x + b y = c a b a b a b a b 6 3
0 = 0 0x - 5y = 5 0 x + 0 y = A { B 6y - 4x = - 0 { { x - y = C x - y = D x - y = - x - y = 4 x + 4y = 0 0 A B - = 0-4 D C x - y = x - y = x - y = - 4 C { 0 x + 0 3y = 7 3 4 x - 5 y = 3 ax + by = c a b c a b 0 a b x + 3y = 70 3 { 5x - 4y = 60 4 x y 7
{ y = 0 x = 0 ax + by = c a b c 3 { x - 3y = 8 3y + z = 0 x - z = - 3 x z - z 3 + x y x - 3 + y z 3 z 3 x y z + y - 3 x y z z 獉獉獉 + 3 { x - 3y = 8 x + 3y = - 4 { x = y = - z = 3 5 3 4 8 x - 3y = A { 0 x - 0 3y = 0 x - 3y = C { - 0 x + 0 3y = 0 { 0 4x - y = 6 B - x + y = - 5 { 0 4x - y = 6 D x + y = - 5 x + y - = 0 x + y - = 0 x - + - y = 0 3 x - - 3y + = 0 4 A B 3 C 4 D 4
{ 0 x - - 0 05 - x + y + 3 = 5 - y - 5-3 y 3 3 x - y = 3 4 3x - y - z = - 7x + y = - 3 3 5y + z = - ( ) [ ] + x 5 89 8 6 4 6 7 6 8 0 0 3 3 9 x - ax + bx + c 5 8 a b c 0 { x = 3 { x = y = 8 x y ax + by = a b y = 4 9
& 7 > 0-5 < 4 x + 3 > x + x - 5 - x < 獉獉獉 3 3 30
x - 3 > 0 3 x > x > x - - x > 5 6-6- 3 5x > x - 5 x + < - x + 5 > x x < 0 3
5x < x x = 0 5x = x x > 0 5x > x 5x > x x + - 5 < - x + - 5 x + < - x + - 6x x - 3-6x x 3 > < a + b a - b 3-6 - 3 3-6x - 6 x - 3-6x 3 b < 0 a + b < a - b b = 0 a + b = a - b b > 0 a + b > a - b b < 0, b < 0 b < 0 b + b < 0, b + b - b < 0 - b b < - b, a + b < a - b b = 0 b > 0 b < 0 > - b < - b b < 0 - b > 0 b < - b 3 3 3 x - 4x + 3 x 3 6x - 6 8x + 6-8x + 6x 6 + 6 - x x - 6 3 x - 4x + 3-6 - 5-4 - 3 - - 6-
4 6- x - - 4x + - 5-5 > - 5-6-3 - x - - 4x - - > 5 5-6 x - - - 4x - > 5-6x + 6 + 4x + > 5 - x > 8 x < - 4 6-3 x > a x < a x a x a a > = > = < = 5 3 5 + x { 6x - < 3 5 + x 33
x - 6x - < x < 6-4 6-4 - x < 3 5 + x - x 5-3 - x x - x 3-5 x - x x - - x < 6-5 6 6-5 x + > 3x > x + > 3x { 3x > 5 3 < x < x + y = 3x - y = 3 x + y = 3x - y x + y = x + y = 3x - y { 3x - y = { 3x - y = { x + y = x + > 3x > 34
{ 3x > x + > { x + > x + > 3x x + > 3x { 3x > 6 a > b c < 0 a + c > b + c a 3 - c > - b c ac > bc 4 ac < bc A B C 3 D 4-5 3 a > - 7 a + c > A a - c > a + c B c - a > c + a C ac > - ac D 3a > a > < 3 5a < 5b 6b - a 0 4 x + y 0-5x 0y 5 a 0 b < 0 - ab 0 n 6 m - 3n m + 3n - 8 - n 7 7-3ab < - ab a < - 8a 5b - b 8 0 mn 0 mp a + m < a - m 3n - 3p 0 9 x - x + - x - - x - 0 0-4 x - - x - x - 4 + x x { - 6 < 7 x + 5 6 - x - 59-8x x 3x - - x x 35
- 3x 3 = - 3x 3-3x 3 = - 3-3 x 3 + 3-3x 3 = - 3 x 3 5x - x - x + - x - 3 = 5x - x - 4 - x - 6x + 9 5x - 6x - 3x + x = 5x - 6x - 8x + 6x 3 3 5x - - 3x 6x = 5x - 6x - 8x = 5x - x - 4 - x - 6x + 9 = 5x - x + 4 - x + 6x - 9-6x = 5x - 6x + 8x - 6x 3 6x = 5x - 6x - 8x + 6x 3 3 = 5x - 6x - 8x 36
a 3 a 3 a 3 + a 3 3 3-7x 3x - 5x + + ( ) 3 a n - a 3n - a 8n - a n 4 x 4-3x 3 - x = a 6 a 3 3 = a 6 8a 9 = 8a 5 = - 7x + 3 3x - 5x + = - x 3 + 9x + 35x - 5x - 4x + 6 = - x 3 + 44x - 9x + 6 3 = a n - a 6n + 4a 7n - = a 7n - + 4a 7n - = 5a 7n - 4 - x + 3 ) - x - 3 x 4 + 0 + 0-3x + 0 x 4-3x + 3x - 3x + 0 3x - 9-3x + 9-7x + 3 3x - 5x + - x 3 + 9x - 5x + 6 3 3n = 6n n - + 6n = 7n - 8n - n + = 7n - - x 3 4 x 4 - x - 3x 3 = - x = ax + b x + c - bx = - 4x + 7 - x + x - + x a b c = ax + acx + bc = - x + x + 37
bc = c = - { a = - { a = - ac = b = - - 4x + 7 x + x - x + x - - 3 - a n + - a n - a 3n + a n = - a n + - - a n + a n + a n = a n + + a n + + a n = - a n + + - a n = - a n + + - a n + - a n + - a n = a n + + a n + + a n = - a n + + a n = a n + + a n = a n + + a n + a n + a n = a n + + a n + + a n = - a 3n + - a 3n a n + a n = a 6n - a 5n + a 4n = - a 3n - a n = a 3n - a n = a 6n - a 5n + a 4n + - a + b a - b 38 4 x - y - x - y - x - y - x - x - y y + x - x - y - - x + y 3 a - b a + b = - x - y x + y - x - y - x + y - x - y x + y = - x - 4y + x - y - x - y x + y = - x + 4y + x - 4xy + 4y - x - 3xy - y = - x - xy + 0y = - y + x - y - x - x - y - x + y - x - y x + y = 4y - x + x - y - x - 3xy - y = - x + - y - x - + y = - x + - y - x - - y = - x - - y = x - - y + y = x - + y - y 3 = a - b a + b = a - 4b = a 4-8a b + 6b = a - 4ab + 4b a + 4ab + 4b = a + ab - 4ab a + 4b + 4ab
x - y x + y x - y - x - y x - y - x a + b a - b = a - b a ± b = a ± ab + b x - y - x - - = - - - - a ± b = a ± ab + b a + b a - b = a - b - a + b a - b = a - b a ± b = a ± ab + b a + b a - b = a - b a b 5 a ± b 3 a + b + c a ± b 3 = a ± b a ± b = a ± ab ± b a ± b = a 3 ± 3a b + 3ab ± b 3 a + b + c = a + b + c = a + b + a + b c + c = a + b + c + ab + bc + ca a ± b 3 = a 3 ± 3a b + 3ab ± b 3 ± b a + b + c = a + b + c + ab + bc + ca a b c 6 6 - x - y + 3 - x - y + z y - + x - z - x a - y b 3 c - = - x + - y + 3 + - x - y + - x 3 + - y 3 = x + 4y + 9 + 4xy - 6x - y = - x + y - z - x + y - z - = - x + y + - z + - + x y + x - z + x - + y - z + y - + - z - 39
7 x + x 3 A x B 6x 6 C 8x 8 D 8x 6 - a n - a A a n + a n + a B a n + a n + + a C a n - a n + + a D - a n - a n + - a 3 a - 3 a - 6 - a + a - 3 A - a + 4 B - 4a - 4 C - 4a + D 4 4 3a 3m 3 a m A a 3 B a m C 9a 3 D 9a m 5 - - x + + 4x A - 8x 3 B - - 8x 3 C - - 4x - 8x - 8x 3 D - + 8x 3 6 a + a 3 = a 5 7 a + a = a 8 a + 3b = 5ab 9 a 3a 3 = 6a 6 0 xy 3 = xy 6 a b 3 = 6a 6 b 6 3a 3 b 3 = 9a 9 b 9 3 a 6 a 3 = a 4 m m = 0 5 a n a n = a n 6 a n a n = a 7 x + y = x 4 + y 4 - ( ) 8 a a a + a 9 4a n + - 3 4 a n 0 - a k 3a 3 a 3-7a 3 x - x - x - x + x - x - x + x + 3 3x 3 + 0x + 3x - 7 x + x - 3 4 x + x 3 - x - 5 3x + 5x - 5x - x + 4 6 A x - x + x + x - 4x - 3 A 7 x 4 + x 3 - x + 3x + B x + 3x + x - B 8 x 4 + x 3 + 3x + ax + b x + x + 3 a b ( ) 9-3x 4 y 3 3-3 xn y = 8x 8 y 7 n 30 A= 9x 4 - x 3 - x + x - B = 3x 3-5x - 4x + A B 40
( ma - mb + na - nb = m a - b + n a - b 3 6a b + 3ab + 3a - x n y n + 8x n y n - 3 0 y - x - 5 x - y - 0 x - y 3 3 x - y y - x x - y - y - - + y - x = - x - y = x - y = 3a ab + b + n - n = n n - n - = = - 6x n y n - x n y - 3 3 = 0 y - x - 5 - y + x - 0 - y + x 3 = 0 y - x - 5 - y - x 3-0 - y - x = 0 y - x - 5 y - x + 0 y - x 3 = 5 y - x - 3 y - x + 4 y - x = 5 y - x 4x - 8xy + 4y - 3x - 3y + 4
0 3-7 9 x + 4y m 6-64 3-4x - 5 4 4 a 4 + b 4 = - ( ) 6 9 x - 4y = - = 4y - 6 9 x = y + 4 3 4 ( 3 x + 4 y) ( 3 x - ) ( ) ( ) y x y - 4 x 3 = m 3 + 8 m 3-8 = m + m - m + 4 m - m + m + 4 = m - 4 m 4 + 4m + 6 = m + m - m 4 + 8m + 6-4m = m + m - m + 4 3-4m = m + m - m + m + 4 m - m + 4 3 = + 4x - 5-4x - 5 = + 4x - 5-4x + 5 = 4x - 4 6-4x = 8 x - 3 - x 4 = a ( ) + a b + b 4 - a b = a ( + b ) ( ) ( ) = a + ab + b a - ab + b - a b = 4 a 4 + 4b 4 = 4 a + 4a b + b - 4a b = 4 a + b - ab = 4 a + ab + b a - ab + b Ⅰ Ⅱ Ⅲ a - b = a + b a - b a 3 ± b 3 = a ± b a ab + b - 4 4n - : 000 4: 64: 34: 4 3 3 3 8a b - a 4 b - 8b 3 x 6-7 + 6x 3 3 4a x - x + 4a x - x - x - x 4 a 4-3a b + 4b 4 = b 4a b - a 4-4b = b - a 4 + 4a b - 4b
= - b a 4-4a b + 4b = - b a - b = x 6 + 6x 3-7 = x 3 - x 3 + 7 = x - x + x + x + 3 x - 3x + 9 3 = 4a x - x + 4a x - x + x - x = x - x 4a + 4a + = x x - 4a + 4a + = x x - a + 4 = a 4-4a b + 4b 4-9a b = a - b - 3ab = a + 3ab - b a - 3ab - b 3 Ⅰ Ⅱ - Ⅲ Ⅳ Ⅴ a ± ab + b = a ± b u = x - y 6 x - y - 5 x - y + = 6u - 5u + u x - y 3 3 4 4m 4n m n a b a > 0 b > 0 ab p ± q - r 4 a 4 + 3a b + 4b 4 x 4 - x + x 4 + x + a 4 + 5a b + 4b x 4 - x + 4 x - y - + y - x - y + - xy 3 x - - y + xy 5 x 3 + x - 6x - 8 4 x + y + + x y = x - y - y + = x - y - = x + y - x - y - = x + y - x - y + = - x - xy - y = - x + xy + y = - x + y = + x + y - x - y 3 = x - + xy - y = x + x - + y x - = x - x + + y 4 = x + + x y + y = x + + x y + y = x + + y x + = x + + y 5 = x 3-8 - 6x +x = x 3-8 - 6x - x = x - x +x +4-6x x - 43
= x - x + x + 4-6x = x - x - 4x + 4 = x - 3 Ⅰ 4 a ± ab + b = a ± b Ⅱ 3 4 3 3 4 4 4 3 5 a 3 ± 3a b + 3ab ± b 3 = a ± b 3 4 = x 3-6x + x - 8 = x - 3 5 x 3 - x - xy - y - y 3 = x 3 - y 3 - x - xy - y = x - y x + xy + y - x + xy + y = x + xy + y x - y - Ⅰ 5 3 a 3 ± 3a b + 3ab 3 ± b 3 Ⅱ 6 mx + my - x - y + mz - z m - n - p + - np - m 3 a 4 - a - a 3 + ab 3 + ab - ab 4 x - 4xy + 4y - x + y - = mx + my + mz - x - y - z = m x + y + z - x + y + z = x + y + z m - = mx - x + my - y + mz - z = x m - + y m - + z m - = m - x + y + z = m - m + - n + np + p = m - - n + p = m - + n + p m - - n - p 3 = a a 3 - a - a + b 3 + b - b = a a 3 + b 3 - a - b - a + b = a a + b a - ab + b - a + b a - b - a + b = a a + b a - ab + b - a + b - 4 = x - y - x - y - = x - y - x - y + Ⅰ 3 Ⅱ 4 Ⅲ 3 44
Ⅳ a ± ab + b = a ± b 4 7 x 3 + x - 3 = x 3 - x + 3x - 3 = x x - + 3 x - = x - x + x + 3 = x 3 - + x - = x - x + x + + x - = x - x + x + 3 = 3x 3-3 - x 3 + x = 3 x - x + x + - x x - = x - x + x + 3 = x 3 - x + x + x - 3 = x x - + x - x + 3 = x - x + x + 3-3 - 3 3-3 x = x - x 3 + x - 3 = x - x + x + 3 x 5 + ax 4 + bx e + cx + dx + l x 5 + ax 4 + bx 3 + cx + dx + e = x - m x 4 + fx 3 + gx + hx + i x = m - m i = e m e 8 a - a - a - 3 a - 4-3 a - a - 4 = a - 5a + 4 a - a - 3 = a - 5a + 6 m = a - 5a = a - 5a + 4 a - 5a + 6-3 = a - 5a + 4 a - 5a + 6-3 = a - 5a + 0 a - 5a + = a - 5a + 3 a - 5a + 7 x x - x - x - 3-3 x - x - x - x + 4 + 6 9 x - xy - y + x + 7y - 6 a ± ab + b = a ± b x - xy - y x - y x + y u = x - y v = x + y x - xy - y = x - y x + y - 6 - - 3-3 6 45
- 6, = x - y + 3 x + y - 3x + 3y - x + 4y = x + 7y x - xy - y = x - y x + y = x - y + m x + y + n x - xy - y + x + 7y - 6 = x - xy - y + m + n x + m - n y + mn m + n = { m = 3 m - n = 7 { n = -, = x - y + 3 x + y - x - 4xy - 5y - xz + 6yz - 3z 0 - y 6y + - x - y y - x y - x - x - 5y x + y x = 3 y = - 3 a = 3 b = - 6 a - b 3 - a - ab - b 0 5 a - b 3 - a - ab - b - a - ab - b - a - b a - b 3 - a - ab - b = x - xy + y - y x = 3 y = - 3 = a - b 3 - a + b ( 3 ) - - 3 + - 3 - - 3 = 4 4 3 9 a = 3 b = - 6 ( ) [ ] 3 - - 6 3 - ( ) [ ] 3 + - 6 = 7 7 46
8 A 6a x - y - 3a y - x = 3a a x - y - y - x B 7x - 7y - mx + my = 7 x - y - m x - y C 34x 3 a - b - 5x b - a = x a - b 34x - 5 D a - 33b - 44c = a - 3b - 4c A - 8x + 7 = + 8x + 7-8x - 7 B a - 4ab + 4b - = a a - 4b + b + b - C 64 - x 6 = - x + x 6 + 4x + x 4 D 5 a - b 3 - b - a = - b - a 0b - 5a - 3 4ab a - + b - a 4 x x - y - x y - x + y y - x 5 x n y - x n - y + 3x n + 6 x n y - z m + 4 7 5x 3-5 8 - x + 8x 7 9 7a 3 + 8 - a 6 0 36x - x 4-6 a - 7b - 5a x 4 x + x - 5x x + x + 4 x + x 3 x 3 - x + x - 4 a + b - - 4a b 5 x 3-4x + 5x - 6 x - y - x + 4 7 x + y + 4x y + 4 8 x - y - x - y 9 xy - 3x + 6y - 8 0 ax + ax + a + b + bx + bx a - b + a - c + - bc x 3 - x - x + y 3 + y - y 3 a - ab + b - a + b - 3 4 x 3 - x - 5 a 3 + a - 6 x 3 - x + 6 7 m m - m - m - 3-3 8 x + xy - 6y + x + 3y - 6 9 3y = x + z x - 9y + 4z + 4xz 30 a a - - a - b = - a + b - ab 47
) Ⅰ Ⅱ - Ⅲ - - Ⅳ Ⅰ Ⅱ 3 Ⅰ Ⅱ 4 Ⅰ Ⅱ 3 4 x + x - 4 4 x + x - 4x + x - 48
3 x + x 3x - x + 3 3x - x + 3x - x + 3x - = 0 x = 3 x + = 0 x = - x = 3 x = - x 3 x - 3x - x + 0 3x - 0 x + 0 x 3 x - 3 x x + = 0 x = - x + 3x - x + 3x - x = - x + x + x + x + 3x - x + 3x - - x - y x + y + x + y = x - y x + y = x - y ( ) - x x - - xy xy + - x xy x xy + y - xy = ( - - xy = xy - + xy xy ) = y xy - xy = ( + - x x ) ( - - xy xy ) = x + - x xy - + xy y = x xy xy - x - y x + y - + 49
獉獉獉 b a c - - x 3 x - y x - xy + y y - x x6 - y 6 x - y x - y = x - xy + y - y 6 y - x x6 x - y x - y = x - xy + y - x + y x - y x + y x - y x + xy + y x + xy + y x - y = - x + xy + y = - x - xy - y x 6 - y 6 x 3 + y 3 x 3 - y 3 x + y x - y x 4 + x y + y 4 50 4 a - b a - c + b - c b - a + c - a c - b - x - x + + x x - + x - 7 - x 3 x3 x + - x + x - 4 = a - b a - c + - a - b b - c + a - c b - c = a - b a - c - a - b b - c + a - c b - c b - c = a - b a - c b - - a - c a - b b - c a - + a - b a - c b - c a - b b - c - a - c + a - b = a - b b - c a - c = b - c - a + c + a - b a - b b - c a - c = 0 = - x - x + + x x - + x - 7 - x + = - x - x + + x x - + x - 7 - x + x - x - x - = - x + x - + x x + x - x + - x - 7 x + x -
- x - = x + x - + x x + x + x - - x - 7 x + x - = - x - x + + x x + - x - 7 = - x + 4x - + x + x - x + 7 x + x - x + x - - x + 4x + 5 = x + x - = - x + x - 5 x + x - = - x + 5 x - 3 = x3 x + - x - x + 4 = = x3 x3 x + - x - x + 4 x + - x - x + 4 x + x + = x3 - x 3-8 x + = x3 - x 3 + 8 x + = 8 x + - Ⅰ a - b b - c c - a - a - b b - c a - c Ⅱ - Ⅲ + Ⅳ - b - a + c a - d a b + c - d a - b a + c a - d a = - Ⅱ d ( ) b a - c a + a = - b - c + d a 3 - x x - 4 3 5 5 ( ) - + ( a - b) = ( - a - b ) + + [ ( a - b) ] ( - a - b) - ( + a - b) = - a - b + + ( a - b) - a - b - - ( a - b) = ( - a - b ) = - 4 a - b ( ) - + [ ( a - b) ] - a - b = - a - b + a - b [ ] a - b + 5
( ) = - a - b + a - b - - ( ) a - b - a - b = - 4 a - b Ⅰ ( ) ( ) a = 4 b = 3 - - + 4-3 4-3 4 = - 4-4 - 3 = - 4 獉獉獉 x 6 - y 3 = 9x + y - 8 9x - y - 8 x - y = 3 5x + xy - 5y x - xy - y 3 a + b = a + b b a + a b 3x - y = 6 x = y + 6 3 9x + y - 8 3 y + 6 + y - 8 = 9x - y - 8 3 y + 6 - y - 8 = 7y 5y, y = 0 = y 0 = 7 5 x y 5x + xy - 5y + xy - 5y xy = 5x x - xy - y x - xy - y xy = = ( ) ( ) - 5 x - y - x - y + - 5 y + - 5 x y - - x = - 5 3 + - 3 - = 7 3 ab a + b ab a + b 0 b a + b + a a + b = a + b ab ab a + b = - ab ab a 0 b 0 - = - b a + a b = Ⅰ 5 Ⅱ Ⅲ Ⅳ 3 Ⅱ Ⅲ
7 x x - + x + = 0 x - x x + + x + x = 3 a ax - = b bx - a ± b x x - - x + x + x - = 0 x + x - x x + - x + = 0 x = x + x - = 0, x x + + x x + = x + x + x = x + x = x +, 3 a + b a - b x = a - b a ± b a + b 0 a - b 0, a + b a - b 0 a + b a - b x = a + b x + x - x 3 x a - x - b + = a 0 b - 53
8 { x + y - x - y = 4 { - 3x = 4y x - y x - y - 3 x + y = - 5-6x - 8y = y - x u = x + y v = x - y u - v = 4 { v - 3u = - 5 u v x y u = x - y v = 3x + 4y 9 n m m + n n A n m = n m B m + n = m + n C n m = n m D n m = n + m + n m m + n n A n m = n m B m + n = m + n 3 - - x a A - a ( ) 4 - - mn mn + x a B - x a mn C n m = n m C a D n m = n + m + D x - a A - mn B mn C - D - + mn 5 - A x + 54 - x - x - B x - C x + D x - x 4x + 6 x - x - 5 x + x 7 - x x 6 + x - 5
8 x + x = + x 9 x x + = + x - b 0 - a + b = b a + b - a + b - c + - - + + x x 3-4 x x - 9-3 - x + x + 6x + 9 x - 8 x - 9 - x - 7 x - 8 - x - 5 x - 6 + x - 4 x - 5 ( ) 5 m + mn m - n - ( ) n m - mn m + n + n 6 x = y 3 = z 4 x + y + z x + z a 3 + b 3 7 a + b = - 6 ab = 7 ab 8 x + x + + x + 5 x + 4 = x + 4 x + 3 + x + 3 x + 9 8 0 8 = - bc + ac - ab abc 55
!* a ± 槡 a x = a x a 0 0 a 槡 ± 槡 槡 3 a 槡 a x 3 3 = a x 0 槡 - a = - 槡 3 a x 3 = - a x = 槡 3 - a - x 3 = a - x 3 = a - x = 槡 3 a x = - 槡 3 a 3 槡 - a = - 槡 3 a 6 6 ± 4 6 - 槡 6 - 槡 6 7 槡 534 = 745 75 槡 34 = 8 680 槡 7534 0 槡 07534 槡 7534 = 槡 75 34 00 = 槡 75 34 槡 00 = 8 680 0 = 86 80 槡 0 07534 = 槡 7 534 0 0 = 槡 7 534 槡 0 0 = 745 0 = 0 745 0 槡 9 A ± 槡 9 B ± 3 C 3 D ± 槡 3 A B C 0 D 0 56
!! 槡 a = a = { a a 0 - a a < 0 槡 a = a a 0 00 b 槡 - a b - a b < 0 - a b 0 a 0 b 0 x 槡 + - = - - b - 槡 a b = - 槡 - b - a b = - 槡 - a b x { x + 0 5 - x 0 槡 5 - x 槡 x - 3 槡 x - - x { - 5 x 5-3, - x 5 { x 0 槡 x - 0 { x 0 x 4 - -, 0 x < 4 x > 4-57
3 x - 0 { 槡 x - 0, x > 槡 x + - 槡 - x 槡 - x - x 0, x = - x - - 槡 - x x - { x + - 槡 - x - < x 3 x 槡 3-3x y + 3xy - y 3 y < x y < x, x - y > 0 x y 5 3 槡 45ab = 槡 x - y 3 = 槡 x - y x - y = x - y x 槡 - y x y 5 5ab = 槡 3 5ab 3 5 ab = x y 4 5aby 3 5 a 4 槡 b = xy 5 5ab 槡 aby Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ 4 槡 4 - 槡 5 8 - = 槡槡 3 5 = 槡 槡 3 - 槡槡 3 5 + 槡 5 = 槡 3 - 槡 5 槡 槡 = 槡 5 槡 - 槡 3 槡 = 槡 0 槡 - 槡 6 a + a 槡 - a ± 槡 b = 槡 b a - ± 槡 a - b 槡 槡 槡 ( ) 4 + 4 = 槡 - 5 4 - - 槡 4-5 = 槡 0 - 槡 6 槡 槡 Ⅰ - 58
Ⅱ 0 a - b 3 5 槡 4 - 槡 + 槡 3 - 槡 6 3 槡 4 - 槡 + 槡 3 - ( 槡 6 ) 槡 6 = 槡 6 - 槡 6 + 3 槡 6-3 槡 6 = 3 槡 6 ( ) = 槡 6 - 槡 6 + 3 槡 6-3 槡 6 槡 6 = 3 槡 6 槡 6 = 9 3 = 槡 4 6-6 + 6-6 = - 3 + - = 9 槡 槡 3 槡 6 6 d a 槡 b 3 c bc a 槡 c d = 槡 bc ab 槡 b 3 c 槡 bc = d 槡 bc ab c d b 3 = 槡 c a 槡 b 3 c b 槡 3 c = bd 槡 bc ab 3 c = d 槡 bc ab c = b 槡 c a 槡 c = b槡 c a 7 槡 6 + 槡 5 槡 6 - 槡 5 槡 5 + 槡 3 - 槡 6 槡 5 槡 6 槡 5 = 槡 6 + 槡 5 槡 6 + 槡 5 槡 6 - 槡 5 槡 6 + 槡 5 = 6 + 槡 30 + 5 = + 槡 30 59
= 槡 5 - 槡 3 - = 槡 5 - 槡 3 + 槡 5 + 槡 3 - 槡 5 - 槡 3 - + 槡 3 = 槡 5 - 槡 3 + - 槡 3 + 槡 3 - 槡 3 = 槡 5 - 槡 5 + 3 槡 3-7 a + b a - b = a - b a - b = 槡 a - 槡 b 槡 a + 槡 b 槡 b - 槡 a 槡 a + 槡 b 8 x y x y y = x 槡 - + x 槡 + + x + 槡 - x x y y x + 0 x - x + x 槡 - + 槡 x + + 槡 - x 槡 x - x 槡 + 槡 - x x - 0 { - x 0 x { x x = x = ± x - { x =, x = y = 槡 9 槡 + 槡 + 槡 + 槡 3 + 槡 3 + 槡 4 + + 槡 99 + 槡 00 7 = 槡 - 槡 + 槡 3 - 槡 + 槡 4 - 槡 3 + + 槡 00 - 槡 99 = 9 60 - < x < 槡 x - + 槡 x + + 槡 x - 3 A x - B - 3x C - x D - x + 6 a b c - < a < - b < - 3 < c < 3 槡 a - a + b + 槡 c - a + b + c A c - a B a - b C - a D a a + b 3 - < a < b 槡 b -
A a + b b - B - a + b b - 4 a = + 槡 3 - a + a - a - 槡 a - a + a - a C ± a + b b - D a + b b + A 3 B + 槡 3 C - 3 D - - 槡 3 5 槡 - 槡 3 + 槡 3 - 槡 = 6-3 < x < 槡 x - 4x + 4 + 槡 x + 6x + 9 = 7 槡 a - 4 = 槡 a + a 槡 - 8 槡 4 - a = 槡 a + a 槡 - 9 槡 m = m 0 槡 x 4 - x + = x - m 槡 + 4 = m + 5 - x 槡 x - 3 = 槡 5 - x 槡 x - 3 3 槡 x - 5 + x - 4 a + 槡 a - 5 槡 0-3 00 槡 0 + 3 00 6 x b 槡 a - xy a 槡 ab + b a ( a 槡 b ) x y b 槡 a 7 槡 x + y - 槡 xy ( 槡 x + ) 槡 y x 槡 xy + y + y ( 槡 xy - x - x + y ) 槡 xy 槡 8 7 3 7 - 槡 50 + 0 槡 + 槡 7 + 槡 5 9 a + b - a - b = 4ab 槡 6 + 槡 3 + 槡 - - 槡 6 + 槡 3 - 槡 + 0 x - = - 槡 3 - y x + y x 0 < 槡 x - < 3 x a = 3 + 槡 5 b = 3 - 槡 5 a b - ab 3 x = 槡 - 槡 + y = 槡 + 槡 - x - y x + y 4 x + < 0 4x 槡 - x + 9 - 槡 + 4x + 4x 6
!" x ax + bx + c = 0 b = 0 a c Ⅰ Δ = 0-4ac Δ Ⅱ ax + c = 0 a c ax + c Ⅲ x c = - a a c - c a ax + bx + c = 0 a 0 c b = 0 c 0 x = ± - 槡 a a c a c b c = 0 b 0 x x = 0 x = - a 3 b c Ⅰ a = x + px + q = 0 x = - p ± 槡 p - 4q p - 4q 0 p - 4q < 0 Ⅱ a b - 4ac 0 = - b ± 槡 b - 4ac b - 4ac < 0 a x a c 6 Ⅰ Ⅱ a b c a b c Ⅲ a
獉獉 3 4 a b c Δ a b c Δ 3 a b c Δ 0 < 0 > 0 = 0 3 4 x + x x x x x + 4 x + x x 5 x + x 3-4x x - 4 x a + a = a x + x x x x x x + a x + a = x x + a x + x + a x + x = x + x - x x x - x = x + x - 4x x x 3 + x 3 = x + x x - x x + x = x + x x + x - 3x x x 3 + x 3 = x + x 3-3x x x + x a b c x x x + x x x x + x x x x x a b c x + x x x b x + x = - a x + x = b a a 0 x 63
kx + 8k + x + 8k = 0 k A k > - 6 B k < - 6 C k - 6 D k > - 6 k < - 6 k - 6 k x k x 3 3 Δ Δ = 8k + - 4 k 8k = 6k + > 0 6k + > 0 k > - 6 a 0 8k + 0-6 < k < - 8 k > - 8 D 槡 x - x - 4 = - - 槡 x - 4 = 槡 6-3x + 槡 x - 5x x = 槡 6-3x 6 槡 + 3 + 6 x - 4 = 0 6-3x = 0 x - 5x + 6 = 0 x 3 槡 5x - 0 - 槡 - x = 槡 x - 3 x x x 3 3 槡 5x - 0 - 槡 - x = 槡 x + 3 - 槡 5 x 3 64
4 槡 3x - + 槡 5x + 4 = 槡 x + 5 3x - + 槡 3x - 5x + 4 + 5x + 4 = x + 5 槡 3x - 5x + 4 = - 6x + 槡 3x - - 槡 x + 5 = - 槡 5x + 4, x = 3 3x - - 槡 3x - x + 5 + x + 5 = 5x + 4 - 槡 3x - x + 5 = 0 ( x = - 5 ) 3x + x = 5x 3x 槡 - x 槡 + 5 槡 5x + 4 5x 3 65
a x + b xy + c y + d x + e y + f = 0 a b c 0 { a x + b xy + c y + d x + e y + f = 0 a b c 0 Ⅰ x x y Ⅱ Ⅲ 8 9 Ⅳ a ± ab + b = a ± b a ± ab + b = a ± b m a + b = ± 槡 a - b = ± 槡 m Ⅲ Ⅳ a ± ab + b = a ± b Ⅴ Ⅲ Ⅵ 66 3 3 4 ( ) - 0 x + 0 4x - 0 0 = 0 x - + 槡 3 x + 槡 3 = 0, x = x = 5 0x - 7x + = 0 x - 5x - = 0
x - + 槡 3 x + 槡 3 = 0 Δ = + 槡 3-4 槡 3 = 7-4 槡 3 = - 槡 3 + x = 槡 3 ± 槡 - 槡 3, x = x = 槡 3 x - x - 槡 3 = 0, x = x = 槡 3 3 a + b - 4ab = a - b 4 x - x - 3 = x x -, x = - x = x 3 = - x 4 = 3 x 4 - x 3-7x + 8x + = 0 x 4 - x 3-8x + x + 8x + = 0 x x + x - 4 + x + x + 6 = 0 x + x 3-4x + x + 6 = 0 x + x 3-4x + 4x - 3x - 6 = 0 x + x x - - 3 x - = 0 x + x - x - x - 3 = 0 x + x - x + x - 3 = 0 8 x - x - = x - x x - x - 8 x - x + = 0 u = x - x u - 8u + = 0 u - u - 6 = 0 u = x - x = x - x - = 0 x = - x = u = x - x = 6 x - x - 6 = 0 x 3 = - x 4 = 3 u 67
, x = - x = x 3 = - x 4 = 3 x - x - x - x - 6 = 0 x - x - x - x - 6 = 0 x + x - x + x - 3 = 0 3 3 x - x - = x x + + - x 3 x + x - = x + x -, x = - x = 4 x - 3x - 4 = 0 x x + - x - - 4 9 3 x - x - - x x + - - x = 0 x + x - 4 x + x - = 0 x + x - 4 x + x - = 0 x - 4 x - = 0 4 3 槡 x - 槡 ( ) - 5 槡 x - 3x - = 9 3 槡 x - 槡 ( ) x - 6x + 9 x - 3x - 68
x - 6x - 5-5 x - 3x - - 5 槡 x - 3x - = 0 槡 x - 3x - - 3 = 0 x 槡 - 3x - - 5 槡 x - 3x 槡 x - 3x - + = 0 槡 x - 3x - 0 x - 3x 槡, 槡 x - 3x - - 3 = 0 - + x 槡 - 3x - - 3 = 0 - + = 0 x 槡 - 3x - - 3 = 0 x 槡 - 3x - = 3, x = 5 x = - 5-5 6 x - x + 3 = 5 x - x - x + x + x - + x - x - = 0 x - x + 3 x - x + x - x + - x - x = x x - x - x x x + x x - x - u = x - x + 6 u + = 5 u - u = - 3 u = 5 x - x + = - 3 x - 4x + 7 = 0 Δ = 4-4 7 < 0 x - x + = 5 x - x - 3 = 0 x = - x = 3 x x - - x - - = 0 x x u = x - u - u - = 0 u = - u = x u = x - = - x + x - = 0 x = - + 槡 5 x = - - 槡 5 69
x u = x - = x - x - = 0 - ± 槡 5 ± 槡 7 4 + x 3 = 槡 7 - x 4 4 = 槡 7 4 3 u = - u = 5 x = - x = 3 u = - 3 u = 5 6 - x + x - - x + x + - x + x - = 0 x - x + = 0 Δ = - - 4 < 0, - x + x + = 0 x - x - = 0, = - x - - 槡 3 x - + 槡 3 x = + 槡 3 x = - 槡 3 ax + bx + c a 0 ax + bx + c = 0 a 0 ax + bx + c = a x - x x - x x - x x - x a ax + bx + c a 0 a c a c a c b Δ 3x - y = 8 7 { x - xy + 4y - = 3 Ⅰ 70 y = 3x - 8 x - x 3x - 8 + 4 3x - 8 - = 3 3
x = x = 5 3 y = 3-8, { y = - x = = - y = 3 5-8 { x = 5 y = 7 = 7 x 3 3 獉獉 x + 3xy + = 0 8 { 5x - 5xy - x - 9 = 0 x : 5 3: - 5 x x x y xy y 5 + 0x - x - 9 = 0 x = x = - 9 0 { y = - x = { y = 8 70 x = - 9 0 x + 3xy + y + 3 = 0 9 { 5x + 5xy - x - 5y + 7 = 0 5 - x + 0y + 8 = 0 x + 0y + 8 = 0 3 { x + 3xy + y + 3 = 0 7 { y = - x = { y = - 67 70 x = 7 3 0 x - xy - y = 0 { x - y + 4x - y - = 0 3 3 7
x - y x + y = 0 x - y = 0 x + y = 0 x - y = 0 3 x + y = 0 4 { x - y + 4x - y - = 0 { x - y + 4x - y - = 0 3 x = y 5 4 x = - y 6 y + 6y - = 0 y = 5, - 3 + 槡 y = - 3 + x = 槡 - 3 - 槡 - 3 - x = 槡 = - 3 + 槡 = - 3 - 槡 { x = - 3 + 槡 { x = - 3 - 槡 y = - 3 + 槡 y = - 3 - 槡 y + 6y + = 0 y 6 = - 3 + 槡 y = - 3 - 槡 x x { 3 y 3 = 3 - 槡 = - 3 + 槡 = 3 - 槡 x = 3 + 槡 x { 4 y 4 = 3 + 槡 = - 3 - 槡 x - 4xy + 4y - 9 = 0 { x + xy - 3y + x + 7y - = 0 x - y = 9 x + 3y - x - y + = 0 x - y = 3 x - y = 3 x - y = - 3 x - y = - 3 { x + 3y - = 0 { x - y + = 0 { x + 3y - = 0 { x - y + = 0 0 a ± ab + b = a ± b x - xy + y - = 0 { x + xy - 3y - 3 = 0 a ± ab + b = a ± b 7 3 - x - 7xy + y = 0 x - 3y x - 4y = 0 x - 3y = 0 x - 4y = 0 3 { x + y = 5 x - y = 5 x - 3y = xy = 6 { 3 xy = 6 { xy = x y p - 5p + 6 = 0 x = p = { y = p = 3 x = p = 3 { y = p =
x = x = 3 { y = 3 { y = x + - y = 5 { x - y = - 6 x - y p - 5p - 6 = 0 x = p = 6 { - y = p = - x = p = - { - y = p = 6 x = 6 x { = - y = { y = - 6 x + - 3y = 3 { x - 3y = - x y 4 x + y = 3 { xy = 6 3 x + y = 3 { x - y = x + y = 3 { xy = 6 x + y = 3 { x + y = 5 4 4x + 3y = 9 { xy = + x + y = 5 x + y = ± 5 3 x + y = 3 { x + y = 5 xy = xy = 6 3 3 x + y = 3 { x - y = - xy = - xy = 6 3 4 4x + 3y = 9 { xy = x + 槡 3y = 9 x { 槡 3y x 槡 3y = 4 槡 3 3 3 3 5 x - 7x + = 0 73
( ) x 7-7x + = 0 x + x = - - x x = α β α = x - x = x + x - 4x x = ( 7 ) β = x + x = x + x x x = 7 = 7-4 = 4 4 α + β = 4 4 + 7 = 69 4 4 α β = 4 7 = 87 4 x - 69 4 x + 87 4 = 0 x + x x x x x b x + x - b a - b a 3 獉獉 4x - 69x + 87 = 0 8x - 38x + 574 = 0 4 + - 6 x x - m - x + 4 m + = 0 m x x x < 0 x < 0 m < m 74 - - m - = x + x < 0 4 m + = x x > 0
m <, m - 3 ( ) Δ = - m - - 4 4 m + = - m - 3 0 m < m - 3 m m - 3 4 7 m x x - x + m - = 0 m x x - 3m - x + 5 4 m - m - 4 = 0 Δ = - - 4 m - = - 4m + 8-4m + 8 > 0 m < - 4m + 8 0 m - 4m + 8 < 0 m > ( ) Δ = - 3m - - 4 5 4 m - m - 4 = 4m - 4m + = m - + > 0, m 8 30 cm 0 cm 44 cm - x cm 30 - x 0 - x = 44 x = 9 x = 6 6 cm x = 9-30 - x 0 - x 30 - x 0 - x = 44 30 - x > 0 0 - x > 0 75
x ax + bx + c = 0 a 0 A b = 0 B b = c = 0 C b - 4ac > 0 D ax + bx + c x x ax + bx + c = 0 a 0 A b < 0 B b a < 0 C b a < 0 c a > 0 D b a < 0 c a > 0 Δ 0 3 x ax + bx + c = 0 a 0 A ac < 0 B c = 0 C D ac 0 4 A B C D 5 b - 4ac < 0 x ax + bx + c = 0 6 b - 4ac > 0 x ax + bx + c = 0 7 ac < 0 x ax + bx + c = 0 8 b = 0 x ax + bx + c = 0 76 9 x + = x - 3 0 3 x - 4 = x 4 - x x - - 槡 x + 3 - 槡 = 0 x 4-7x + 0 = 0 3 x - 8x 7 = 0 4 5 x + x = 4 x - 5 x + + 8 x + x 3 + 5x = 0 6 7 3 x - - 3x + 6 = + 4 - x ( ) x x - 8 x + 3x - 9 x 槡 + 5 + - 5 ( ) x x - + 6 = 0 0 x + 3x = 8 槡 3x - 4 + = 0 0 x 槡 - 5 + 4-3 槡 x + = 0 3x + 5x + x + 5x 槡 + - = 0 + 槡 9 x + 4-9 + - 4 = 0 槡 x + 9
3 x x - x - x - 3-4 = 0 4 5 x + + x + = x + x + 3 x + x = x + x + 6 x + 4xy + 4y = 9 { xy + y = 7 xy + y + x + y = 6 { xy + 4y - 3x - 6y + 3 = 0 8 槡 x + + 槡 y - = 5 { x + y = 9 x - xy - x + 4y + 3 = 0 { x - y = 3 30 x + 4xy - x - y = 0 { x + xy + y - x - y = 3 3 x + y = 3 { x - y = - 5 3 4x + 9y = 40 { xy = - 33 4x - 9y = 7 { xy = - 34 k x k - x + kx - k + 3 = 0 35 x x + 3 m - x + m - 4m - 7 = 0 m m 36 x x + px + q = 0 p q 37 x x - a x - b - cx = 0 m n a b x x - m x - n + cx = 0 38 a b c b = a + c x ax + bx + c = 0 39 x x - 5x + 9 40 x x 3x - 8x + 9 = 0 x - x - x - x x x 4 x - 5x - = 0 4 x ax 3 + bx = 4 4 a b 77
43 74 30 90 8 44 0 50 45 4 30 3 46 60 A B 4 40 AB 47 3 48 8 4 8 5 49 3 3 7 50 6 6 3 5 63 8 78
!# 3 3 獉獉 獉獉獉 4 7 t d 0 t d d = 8 t d = 8 t 79
5 0 0 > 0 > 0 tg sec tg sec 90 ( ) k π k ctg csc ctg csc 0 80 kπ k arcsin arccos - - x 0 y 0 x 0 x x 3 0 y x y x x y y x > < 80
4 5 + + - + - - + - x a 0 y 0 a y = x y = - x a - a a x a b a - b y a b - a b a b - a - b y = x a b b a y = - x a b - b - a y = ax b + bx + c a 0 x = - a 4ac - b a > 0 y = 4a 4ac - b a < 0 y = 4a y = ax + bx + c = a x + b 4ac - b ( a ) + a 0 4a ( ) x + b a 0 b, a > 0 x = - a y = 4ac - b b a < 0 x = - 4a a y = 4ac - b 4a y x 8
y y y x y 3 y y y 7 8 40 3 70 3 0 ( ) 40 3 4 70 3 80 3 0 40 3 0 40 3 l l : y = - x x l y = - x l y = kx k ( ) ( ) x = y = - x y = - - x y = kx k = l : y = x y = - x = - 4 l l 3- l l x, = = 3 4 = 90 - = 90-3 = 5, l l y ( ) y = - x - y ( - - ) y = kx k = 3-8
l l l k b l b l l y x = - k l l l l : y = ax + bx + c a 0 a b c 3 x - 6x y = 槡 + 8 x y = 槡 6-6x - x 槡 - 5 槡 - x + 3x + 4 - x lg( x + ) 0 0 0 > > 0 x - 6x + 8 0 x x 4 6x - x - 5 0 x 5 槡 6 6 ± - 6x - x 槡 - 5 0 x 槡 0 x 4 x 5 6 ± x 槡 0 - x + 3x + 4 > 0 - < x < 4 x + > 0 x > - ( ) lg x + 0 x - < x < < x <4 ( ) 4 3 - - 3-3 - - 5-4 - 5 3 ( - 9 4 ) 0 ( - 9 4 ) y = kx + b k 0 3 - - 3, - = k 3 + b { { k = - 3 = k - 3 + b b = 0 y = - 3 x 83
3 - - 3 y = kx k 0 3 - k = - 3 y = - 3 x - 3 - - 5-4 - 5 y = ax + bx + c a 0-3 = a a = - { + b + c 5-5 = a - + b - + c b = - 5 = a - 4 + b - 4 + c c = - 5 y = 5 x + x - 5 ( ) 3-9 4 0 ( ) b - a = - 4ac - b = 4a 4 0 = a + b + c { a = - b = - c = - 9 4 0 - ( ) ( ) 9 4 = a - + b - 0 = a + b + c b - a = - ( ) y = a x + b 4ac - b + a 4a ( ) ( ) - 9 4 y = a x + 0 = a + + c { a = - b = - c = ( ) + 9 4 a = - ( ) y = - x + + 9 4 = - x - x + + 9 4 0 3 84
5 + 槡 0 0 - - 槡 0 x 6 x = - y = x - 3 - y = ax + bx + c a 0 x - 槡 0 + 槡 0 ax + bx + c = 0 x = - 槡 x = + 槡 y = ax + bx + c = a x - x x - x y = a x 0 - - + 槡 x - - 槡 - = a 0 - + 槡 0 - - 槡 a =, y = x - + 槡 x - - 槡 y = x - 4x - y = ax + bx + c a 0 y = x - 3 - y = x - 3 y = - 4 - - 4 3- b x = - a x = - 3- x = - x - 0 x 6 x = - x - - 3 = - 4 - + 3 = - 4 0 0 y = x + x - 4 y = ax + bx + c a 0 a b c x x 0 x 0 y = a x - x x - x a 0 a 6 y = - x - 4x + - 3 x 0 3-5 x - 3 y = - x - 4x + a = - < 0, 4ac - b 4 - - - 4 y = = 4a 4 - = 3 85
y = - x + + 3 - x + 0, x = - - x + = 0 y = 3 x < - y x x - y x y = - x - 4x + y = - x b - 4x + x = - a = - x 4ac - b 4a = 4 - - - 4 4 - = 3 3-3 - 3 < - < 0-3 x 0 y = 3 3-3 x = - x < - y x x - y x x = - 3 x = 0-3 x 0 y = - - 3-4 - 3 + = - 5 3 x - y x - 3 < - - 5 < - - 5 x - 3 x = - 3 x = - 5, y = - - 3-4 - 3 + = - 5 y = - - 5-4 - 5 + = - 9 7 00 3-4 00 3-4 00 3-4 Ⅰ Ⅱ y Ⅲ = x 00 - x 86
( ) y = 00 - x x 0 < x < 00 3 6 x 00 - x - x 8 0 cm 3-5 y y x cm y 槡 0 - x cm y = x 槡 00 - x = 槡 - x 4 + 00x x > 0 m = - x 4 + 00x y u = x m = - u + 00u a = - < 0, u = - b a = + 50 x = 50 x = 5 槡 - 5 槡 y = 槡 m = 50 cm 9 x + 3 x - 4ac - b m = = 500 4a x - > x + 3 x - - 0 - x + 5 x - 0 Ⅰ{ - x + 5 0 Ⅱ - x + 5 0 x - > 0 { x - < 0 x 5 { x 5 x > { x < Ⅰ < x 5 Ⅱ, < x 5 x - x - > 0 x > > x - x < 3 3-5, < x < 3 x - < 0 x < < x - x > 3 x 87
< x < 3 0 x - > 4 x - > - 4 3 x - < 4 4 x - < - 4 5 x - > 0 6 x - < 0 7 x - 0 8 x - 0 x - < - x - > x < - x > 3, x - x 3 - < x - < x - > - { { x > - x - < x < 3, - < x < 3 4, 5 x - 0 x 6, 7, x - x 8 0 0, x - = 0 x = x > 4 x > - 4 x < 4 x < - 4 x > 0 x < 0 x 0 x 0 8 x x - 8 88
x 4 x 4 x > x < 4 > < x x 8 8 3x - > 0 3 x - x + 0 5 x - 6x + 9 0 7 x - 6x + 9 0 - x - 4x + 0 4 4x - x + 0 6 x - 6x + 9 > 0 3 x + x - > 0 x + > 0 { x + < 0 x - > 0 { x - < 0-3x - x x + x - 0 x < - x > < 0 x a a x + 4x - 0 x + 4x - = 0 = - ± x 槡, x + + 槡 x + - 槡 0 - - 槡 x - + 槡 3 x - x + = 0 Δ = - 7 < 0 x - x + ( x - ) + 7 4 0 ( x - ) - 7 4, 4 3 ( x - ) + 7 4 0 89
( x - ) - 7 4, 5 x - 3 0 x, 6 x - 3 > 0 x - 3 0 x 3, 3 7 x - 3 0, 3 3x - = 0 x = ± x - 3 = 0 x = 3 y = 3x - a = 3 > 0 3-6, 3x - > 0 x < - x > - x - 4x + 0 = - ± x 槡 y = - x - 4x + a = - < 0 3-7, - x - 4x + 0 - - 槡 x - + 槡 3-6 3-7 3 x - x + = 0 Δ < 0 y = x - x + a = > 0 y x 3-8 90, x - x + 0 4 3, x - x + 0 5 x - 6x + 9 = 0 x = 3 y = x - 6x + 9 a = > 0 3-9, x - 6x + 9 0 6 5
3-8, x - 6x + 9 > 0 x 3 7 5, x - 6x + 9 0 x = 3 3-9 5 6 7 3 4 - Ⅰ Ⅱ 3 4 Ⅲ 5 6 7 x x - m + x - m = 0 m x x + m - 7 x + m = 0 m = m + ± 槡 m + 0m + 4 x < m + + 槡 m + 0m + < 4 m + - 槡 m + 0m + < 4 9
y = x - m + x - m x - m + x - m = 0 a = > 0 y 3-0 x 0 0 0 x = y < 0 x = y > 0 3-0 - m + - m < 0 { { - m + - m > 0 m > m <, < m < y = x + m - 7 x + m x + m - 7 x + m = 0 a = > 0 y l 3- x 0 0 0 0 x = x = y > 0 3- + m - 7 + m > 0 { { m > 3 + m - 7 + m > 0 m > 3 m > 3 3 3 3- l y l x Δ > 0 m - 7-4m > 0 m - 8m + 49 > 0 m < 9-4 槡 m > 9 + 4 槡 3- l l 3 3 y l x 0 0 b x = - a 0 0 < - m - 7 < 3 < m < 5 3 3 3 < m < 9-4 槡 3 3 9-4 槡 9-4 槡 - 3 3 = 5 3-4 槡 = 7 3-4 槡 - 3 3 > 0 9-4 槡 > 3 3 9 89 89 - 槡 3 = - 槡 9 槡 3 9 = 9 > 3 9
x 0 x 0 x Δ > 0 0 0 x y > 0 y < 0 Δ > 0 3 3 y = - 3x A x y y = 4 x A x y B x y C x y C y x B x y D x y D x > 0 x y x < 0 x y 3 a < 0 b < 0 c > 0 y = ax + bx + c A B C D 4 x = - 3 4 A y = - x + x + 4 B y = x + x + C y = x - x - D y = x - x + 4 5-3 A y = - 3 4 x - 3x C y = - x - 4x - B y = 3 4 x + 3x D y = - 3 4 x + 3x 6 x = y = - x = 3 y = 4 x = - y = 4 A x = 4 B x = - 4 C x = - - 4 D x = - 4 x 7 y = 槡 + lg 4 - x x x 8 y = 槡 - x - 3x - 4 x 93
9 8 R R S 0 y = x t - t - t = t = y = - x - 3x + y x x y x x y 0 x y < 0 x x = - 4 y = 0 x = 0 y = - 3 x = y = 0 3 y = 3x - x 0 x 4 l y = x + y = 3 l 6 5 y = 3x + 6x - 3 - x 3 0 x 3 6 y = A 0 7 - x 3 - x > 5 - x > - 7 - x 0 9 - x > 0 8 - x x + 3 < 9 x + x x + 3 - x 4 - x < 6 - x < - 8 - x 0 0 - x < 0 x + > 0 m x - 3 - x < 0 9x - 6 > 4x - 4 + > 3 - x x { 3x 4x - > 3 x - { x - < x - 4m k x kx - k - x + k - > 0 x + > 3x x { a 3x + a > 0 3 p x x - px + - p < 0 94
!" n n 3 n a a m n 槡 m a > 0 m n n > 3 m m ( ) a m = ( - m ) a ( b - m ) a = b = [ ] ( a m ) b a b 0 [ ] a - m = a = m a a - m b ( a ) ( ) = a b a - b - 5 c 3 b 3 c - m ( ) b a n = ( a - n b ) a b 0 = a - b - 5 c 3 b - 3 c a - b - 5 c 3 = b 3 c - b 3 c - a b 5 c - 3 a b c 0 n 3 kn k n 5 95
- 8490000 0 0000043 3 59 04-8490000 = - 8 49 0 6 0 0000043 = 43 0-6 3 59 04 = 5 904 0 Ⅰ ± a 0 n n n Ⅱ ± a 0 n n ± a 0 n n 0 n n 0 n ( ) 4 6 槡 4x 4-4x + 0 < x < 槡 x 0 6 x 0 槡 44a 0 3 b 8a 0 槡 b 4 槡 x - x + 獉獉 3 8 = 7 7 6 x 0 a 4 b 獉獉 = 槡 4 x - 0 < x < 槡, 0 < x < x < x - < 0, = 槡 4 - x = 槡 - x 6 x ( 5 ) 3 3 x 5 = = 槡 3a 5 b 槡 3a 5 b = x 3 x 3 ab 3a 5 b 3 槡 ab = x 3 槡 8ab x 6a b 6 x 6 x 4 5 a b 4 3 = 7 a 0 b 5 a 4 槡 b = x 6 槡 3a b 4 x 4 4a b x - - x 96
x - 槡 a a 0 a < 0 a - a n Ⅰ Ⅱ n Ⅲ n n 5 a 3 a a 7 a 3 Ⅳ n n 5 a 8 = a 5 a 3 a 7 = a 5 a a 3 n Ⅴ n n n 3 9 x - 槡 3 3 x ( ) x + = 0 9 x + - 0 3 x + = 0 3 x - 4 x + + 3 = 0 3 x = 3 - x + x = - x + x = - 5 3 x + - 0 3 x + = 0 9 3 x - 0 3 x + = 0 3 x - 9 3 x - = 0 3 x = 3 x = 3 0 x = 0 9 3 x = 3 x = 3 - x = - 3 x - x + + 3 = 0 x - 4 x + 3 = 0-3 x + 3 = 0 x = 0 4 - ( ) - 3 ( ) + 6 - + 6-0 75 = - - - 3 + 4 - + - 4-3 4 = - - 3 - - 3 + - + 3 97
= - 3 + 4 + 8 = - 8 + 4 + 8 = 4 ( ) - 3 3 - ( ) 5 5 a - 3 3 b - 3 b 槡 - 6 4 槡 3a a - + b - - + a - + a - b - + b - + ab - - 3 x - + y - x + y - 4 x - x 3 x 3 - x 3 + x 3 - x + 3 3 = a - 3 b 6-5 a - 4 b - 3 5 = a - 3 b 6-5 3 a - 4 3 b - = - 5 3 a - 5 3 b 5 5 = - 3 a - b 3 b = a 3 槡 4a = a - 3 b 6-5 a - 4 b - 3 3 5 = a - 6 5 b 5-5 a - 4 b - 3 5 = a + b = a - 5 b 6 5-3 a - 4 5 b - 5 = - 3 a - 3 b = b a ( ) - ( ) = b + a ab - = ab a + b + a a + b + + a + b - ( a ) + ( b + a b ) - ( ) + ( b + a - ) + a + b a b ( ) 3 = x + y x y a + b = a + b = x - 4 y - 4 = x 4 y 4 b - 5 3 槡 4a x + y - = x + y x y - x + y - ( ) = x - 4 + x - y - + y - 4 x + y - = x + 4 = x + y x + y - = x 4 y 4 x 4 y 4 4 = x 3 x 3 - x 3 - x 3 + x 3 - x 3 + x 3 - x 3 + x y + y = x 3 x 3 + x 3 - x 3 - x 3 + x 3 - x = x 3 3 = 槡 x 3 + x 3 - x 3 + 4 x + y - 98
4 a + b a + b - a + b a + b - 3 4 a n a n = A n = 0 B a = C a = n = 0 D n = 0 a = a = n = 0 a A a 0 = B a > 0 C - a 4 a D a - a = 3 n - - n n - A B C D 4-4 - 3 4 A 8 B - 8 C - 8 D 6 5 a > b a b + a - b = 槡 a b - a - b A 槡 6 B - C - D ( ) 6 槡 - x - 4 = 0 x = 7 9 x - 3 x - = 3 x = 8 槡 x - 3 槡 4 x + = 0 x = - 5 ( ) + 0 5 0 5 - ( 9 槡 3 - ) 槡 - 3 ( - 7) 0 [ - 槡 - ] - ( ) 0 0 槡 3 6 ( 3 ) 4 4-0 槡 - 3 - + - ( 300) a 3 3 b 3 b 槡 4 槡 a a ( ) 3 - xy - 3 3x - y 3-4 x y - 3 4 - b 3 c a - bc - 5 x - 3 5 槡 a - 3 b 槡 b/a 6 x 5 6 y x - 槡 y 3 3 x 槡 y 槡 槡 x 3-99
7 8a - 3 ab - 3 3 ( 4 b ) 4 9 m - 槡 槡 3 n p - - 3 3 xy - 8 x y y ( x ) 0 m - np - 3 槡 - - 4 + 6 5 3 + 槡 - a - + a - + a - - - a m - - - m + m - - m + - m 3 4-6 5 3 a 3 3 3 3 3 3 + b - c a - b + c 4 x - + x - x - x - 5 a + a - a - a - - a + a - x - x 3 x + x 3 + x 3-6 a - a + x - x 7 x + x - = m x + x - 8 x m = 3 x3m + x - 3m x m + x - m 9 a + a - = 3 a + a - a 3 + a - 3 00
!# 0 a b = N a b N a b a N N b a N b a a b = N b a N > 0 a a N b a N b a N a N > 0 a log a N = b log a M N = log a M + log a N M N a > 0 a log a M N = log am - log a N M N a > 0 a log a M n = nlog a M M a > 0 a n log a 槡 M = n log am M a > 0 a n = 0
alog a N = N N a > 0 a lg4 - lg6 lg7 - lg3 lg4 - lg6 lg7 - lg3 log a M - log a N = log a M N M N a > 0 a lg4 lg6 log a MN = log a M + log a N M N a > 0 a lg 4 6 = lg 7 3 lg 7 3 = lg 7 3 = lg7 + lg - lg3 - lg = lg7 - lg3 log 槡 8 log 槡 3 x = - 3 x 3 3 - log 3 5 4 槡 3 3 lg7 - lg3 = lg7 - lg3 = ( ) 6log 3 5 3 4 0 log 槡 8 = x 8 x = 槡 3x = - 3x = -, x = - 6 ( ) - 槡 3 = x 3, x = 3 - - 4 = 3 4 = 槡 3 3 - log 3 5 = x log 3 x = - log 35 = log 3 5 - x = 5 - = 槡 5 5 = 3 log 3 5 -
= 5 - = 槡 5 5 ( ) 6log 3 5 a log a N = N N a > 0 a 4 x = 槡 3 = 3-6log 3 5 = 3-3log 3 5 3 log 3 x = - 3log 3 5 = log 3 5-3, x = 5-3 = 5 = 3-6log 3 5 = 3-3log 3 5 = 3 log 3 5-3 = 5-3 = 5 3 4 a log a N = N N a > 0 a nlog a M = log a M n + 3 lg4400 = 4 6454 lg0 0044 lg0 05 = - 840 lg5 3 lg4400 = 4 6454 lga= 6454 lgb = - 6454 lgc = 3546 lgd = - 3546 lg 槡 E = 37 A B C D E 0 6454 4 lg 09 = 045 lg3 6 = 0 500-3 6-0 03 lg0 0044 = 3 6454 lg0 05 = - 840 = 760, lg5 = 0 760 3 lg4400 = 4 6454 lga= 6454, A= 0 440 lgb = - 6454 = 3546 lg4400 B = lg4400 + lgb = 4 6454 + 3546 = 3, 4400 B = 000 B = 5 lgc = 3546 B C = 5 lgd = - 3546 = 3 6454, D = 0 0044 lg 槡 E = 37 lge = 37 lge = 6454, E = 44 x = 0 6454 lgx = 6454, 0 6454 = x = 44 4 x = - 3 6-0 03 - x = 3 6-0 03 > 0 lg - x = lg3 6-0 03 = - 0 03 lg3 6 + = - 0 045 lg - x + lg 09 = - 0 045 + 045 = 03
lg - 09x = - 09x = 0, - 3 6-0 03 = x = - 0 09 = - 000 09 3 0 n n 5 A log a M + N log a M + N = log a M log a N B log a M log a N log a M log a N = log a M + N C log a M log a N log a M + log a N = log a M N D log a M N log a M N = log a M + log a N lg 53 = 0 4033 lg4 033 = 0 6056 lg 4033 = 0 450 lgx = 4033 x A 450 B 4 59 C 5 3 D 60 56 3 p > 0 p a b b 0 p A - a b C a b B - a - - b D - a - - b + 4 log x 8 = - x = 5 log 7 9 = x x = 6 log x = x = 7 log x x = x = 8 lgx - lgx - 3 = 0 x = 9 lgx = 3lga + lg - 4lgb x = 0 lg3 = 0 477 lg5 = 0 6990 lg 3 + lg64 - lg4 = 3 7 8 5 0 04-63 lg0 0303 = - 588 lg0 303 =
lg7 0 = 854 lga = 854 lgb = - 854 lgc = 854 lgd = 486 lgx = - 486 lgy 3 x = y = = 5 554 a = 3 log 3 - lg0 0 + log 5 槡 5 + 7 log 7 4 lg + log 8 + lg5 - lg 槡 3 0 0 + 槡 7 7 5 lg5 + lg lg50 - 槡 - log 5 log 646 6 5 log3 5 + log 5 lg8-3lg 7 槡 0 + lg 槡 7 lg b = 0 0 854 = ( ) 8 log x - 4 x + 4x = x log 7 4 9 lgx - lgy = a lg5x 3 - lg5y 3 c = d = 05
!$ 0 80 α sinα = y r α p α α sinα α sinα α α α sinα = y r y = rsinα r = y sinα sina = a c a = csina c = a sina y α x p r p A a c sinα = y r cosα tgα ctgα tgα = sinα cosα sin α + cos α = ctgα = cosα tgα ctgα = sinα a sina = b sinb = c sinc 06
a b = sina sinb b c = sinb sinc c a = sinc sina ABC O CA A B A = A A BC = 90 6- Rt A BC BC = A C sina a = RsinA b = RsinB c = RsinC a sina = b sinb = c sinc = R 6- sinb = bsina a 3 Ⅰ Ⅱ Ⅲ 4 ABC C = 90 A= 0 0' b = 4 ABC a = c = 5 ABC A+ B = 90 B a = btga c = b cosa a c 07
b sina= a c cosb = a c A B B b ABC A= 5 B = 6 a = 0 a = 0 b = 4 C = 6 3 a = 7 b = 5 c = 9 C b = asinb sina c = asinc sina b c c c = 槡 a + b - abcosc a b sinb = bsinc B A c 3 cosb = a + c - b B ac sina = asinb b A A+ B < 80 0 80 3 3 08 3 ABC A= 30 b = 8 a = 3 A= 30 b = 8 a = 4 8 3 A= 30 b = 8 a = 槡 3 3 4 A= 30 b = 8 a = 8 5 A= 30 b = 8 a = 8 槡 6 A= 90 a = 6 b = 6 7 A= 90 a = 6 b = 8 8 A= 90 a = 6 b = 3 9 A= 0 a = 6 b = 6
0 A= 0 a = 6 b = 8 A= 0 a = 6 b = 3 sinb = bsina = 4 a 3 >, B 6- AD B sinb = bsina = a, B = 90 6-3 AD 6-6-3 3 sinb = bsina = 槡 3 a, B = 60 B = 0 6-4 AD B B 4 a = b, B = A= 30 6-5 AD A B 6-4 6-5 5 sinb = bsina = 槡 a 4 a = 8 槡 > 8 = b, B < A B B 0 4' 6-6 AD B 6-6 6-7 6 sinb = bsina = a 09
, B = 90 A+ B = 80 6-7 AD A 7 sinb = bsina = 4 a 3 >, B 6-8 AD 8 sinb = bsina = a A= 90, B B = 30 6-9 AD B B Rt AB C 9 a = b A= 0 Rt AB C 6-8, B = A= 0 A+ B > 80 6-0 AD A 6-9 0 sinb = bsina = a 3 槡 3 >, B 6- AD 6-0 sinb = bsina = 槡 3 a 4 6-, B 6 B 54 a = 6 > 3 = b B < A, B 6 6- AD B SSA 6-5 A b > a bsina > a b > a bsina= a 3 b > a bsina< a 4 b = a 5 b < a 3 6 7 8 A 6 b = a 7 b > a 8 b < a 0
4 9 0 A 9 b = a 0 b > a b < a 4 A 45 0 05 9 / A B 4 8 B A 68 A 7 C A3 5 C 99 6 3 D D B 3 A P Q 60 5 5 5 P Q sin5 = 槡 6 - 槡 sin75 = 槡 6 + 槡 ( 4 4 ) A C C 6-3 BAC ABC AB = 0 AC = x BC = 9x ABC C BAC x AE BD EAB ABD EAB = 45 6-3 ABD = 35 ABC = 360 - DBA - DBC = 0 x BAC AC = AB + BC - AB BCcos ABC x = 0 + 9x - 0 9x cos0 A B C 6-4 D CE AB CE F D D ACF AC = 3 5 CAF = 7-68 = 59 6-4 CP AQ PCA QAC QAC = 360-7 = 33 PCA = 47 ACF = PCE - PCA= 5 AFC = 69 CF = AC sin CAF = 3 4 sin AFC CD = 6 3 CD > CF D F 6-5 B BG D B GBD ABG = 80 - QAB = AQ BG ABG + QAB = 6-5 80 ABD ABD BDF
ABD AB = 4 8 AD BAD AD ACD ACD AC = 3 5 CD = 6 3 ACF = 5 ACD AD CAD BAD = CAD - CAB = CAD - 7-68 = CAD - 59 ABD ABD BDF CAF = 59 ACF = 5 AC = 4 8 ACF AF CF AFC DF = CD - CF = 6 3-3 = 3 FB = AB - AF = 4 8 - AF BFD = AFC = 69 BDF ABD 3 PQ PBQ PBQ = 5 + 5 = 30 Q BQ ABQ BPQ BP ABP ABQ 6-6 3 A B DE BC DE BC ABC = EAB = 60 ABQ = ABC + CBQ = 60 + 5 = 75 BAQ = 80 - DAQ - BAE = 60 AB = 5, Q = 80 - BAQ - ABQ = 45 BQ = AB sin BAQ sin Q BPQ PQ = BQ sin PBQ sin BPQ = 5 = 槡 6 BPQ = 80 - Q - PBQ = 05 5 槡 6 槡 6 + 槡 4 = 5 3 - 槡 3 6-6 A B DE BC DE BC ABC = BAE = 60 ABP = ABC - PBC = 60-5 = 45 BAQ = 80 - DAQ - BAE = 60 AB = 5, APB = 80 - BAQ - ABP = 75 BPQ BP = AB sin BAQ sin APB 5 槡 3 = 槡 6 + 槡 4 5 = 槡 - 5 槡 6 Q = APB - PBQ = 75-30 = 45, PQ = BP sin PBQ = sin Q 5 槡 - 5 槡 6 槡 槡 = 5 3 - 槡 3
ABQ ABP AQ = AB sin ABQ sin Q AP = AB sin ABP sin APB = 5 槡 3 + 5 0 = 槡 3-0 PQ = AQ - AP = 5 3 - 槡 3 D 6 α β 0 80 A sinα = sinβ α = β C cosα = cosβ α = β B sinα = cosβ α + β = 90 D α β sinα sinβ ABC sina cosb 0 A C B D 3 α A cosα < ctgα C cosα > ctgα B cosα = sinα D cosα ctgα 4 cm 槡 cm 槡 3 cm A B C D 5 A cm cm 3 cm B cm 3 cm 4 cm C 3 cm 4 cm 5 cm D 4 cm 5 cm 6 cm 6 ABC C = 30 ABC A a = 5 b = C c = 4 a = 3 B b = c = 5 D a = 4 c = 3 3
7 ABC sina= 槡 3 cosb = 槡 3 a b c 8 α tgα = sinα = ctgα = 9 ABC a = 7 b = 3 c = 5 ABC 0 α 0 80 tgα = - 3 P α P y x P α 45 β 50 sinα - tgα cos α - sin α + cosβ cos β - sin β ABC a = 5 b = 0 A= 30 b = 80 c = 5 B = 50 3 a = 400 b = 500 B = 0 4 b = 3 c = C = 45 5 a = 9 b = 0 A= 60 6 a = 7 b = B = 60 7 c = 0 6 b = 0 6 C = 9 3' 3 ABC a = b = c + cosa= 3 5 a c 4 0 ' A= 38 ' B = 74 07' b = 6 a c C S a = 8 c = 6 B = 03 4' b A c S 3 B = 45 a = 5 槡 6 b = 0 A C c S 5 AOB O A 0 - B 6 ABC A a b B a + b + c C 7 ABC C = 90 C y A t B - t 0 t 0 C 8 ABC C = 90 a - b = tga = AB CD ABC R ABC r 9 ABC C = 90 a b c tg A 0 ABC ABC = 45 a = 4 槡 c = 6 AC BM A C D α β A C D m γ α β γ 4
m CD C D C 35 A D 45 5 C 5 B D 45 440 m D 3 A B 00 m CD 6-7 α = 45 β = 60 θ = 30 γ = 5 A B 0 m 4 M 3 5 A M M 8 3' 90 8 M 73 34' 6-7 5
!% 3 7-7- 8 7-7- 7-80 6
7-3 MN 7-3 MN A B C 6 AM AN BM BN CM CN O OA OB OC A C 3 B D 3 C 7-4 a b c a b c d 80 A O B 4 D 7-4 a OB OC OA c OA d 3 AB AB AB AB B A 7
O AB 7-5 AO = OB AO = AB BO = AB = AO 7-5 AB = BO A B AB CD CD C D AB CD O AOC C C A B AB CD AB CD D 7-6 a b c a > c 7-7 AD = 7-6 7-8 AD a c b d 7-7 7-8 AD = a + b - c a AM b AM AB = a c AB BC = b d AC CD = c b AB = a 7-9 7-9 c AM AB BC = b 7-0 BM BC = b 7-8 b c AM
AB = a BC = b d CB CD = c 7-0 7-7 A B C A AB + BC = AC B AB + BC > AC C BC AB - AC D AB + BC = AC BC + CA= BA CA+ AB = CB A C B D 3 A B C D 4 A C 5 A B C AB = BC A AC = 3AB B D B AC = AB C AC = AB D AC AB 6 7- A OB OB > OA 7 7-8 08 9 0 7-3 ABC = 90 BD ABC ABC = 30 BD ABC 7-3 3 9
4 5 6 OC AOB 7 a b a > b a - b - a 8 a b c b > a > c c - a + b 0
!& 獉獉 獉獉, AB CD 8-, = 3, = 4 8- AB CD O, 8-8- 3 8-3
AB CD, = 4 8-4 AOB, + = 80 8-3 AOB, AOB AOB = 80, + = 80 8-4 AOB, + = 80 8-5 a ACBD AB = CD AC = BD AC = BD AB = CD b AOB OE OD COB AOC OD OE 8-5 c d AB MN CE DF ACD CDN PCB CDN CE DF 8-5 8-6 MN DQ AC BC BAN ABQ
MN DQ, BAN + ABQ = 80, BAN + ABQ = 90 + BAN = ABQ, + = 90 = 8-6 BAN AC BAN + = 90 3 8-7 BE DF CBD ADB BE DF C + ADC = 80 BE DF, =, = CBD = ADB =, CBD = ADB, BC AD 8-7 C + ADC = 80 AB 8 8-8 3 = 4 3 8-9 3 = 3 4 AB AD BD 3
8-8 8-9 4 DE AB C FBG DE AB = 0cm C FG 5 8-0 A BC CD B AC DC 6 8- MN A B A B A 3 B 3 C C C 3 = + 3 = 80 A B A 3 B 3 8-0 8-7 8- BD ABC ADC ABC = ADC AB CD BC AD 8 8-3 CD AD AD AB AB BC BC CD 8-8-3 9 8-4 AB CD EP AB P E F CD FP > EP 0 8-5 DE GF BC DE EF DC DC AB B = F 8-4 8-5 4
! 3 3 4 5 3 6 4 5
7 Ⅰ 9-8 0 Ⅱ 9-9 Ⅰ 0 3 6 4
3 3 Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ 3 4 7
4 A ABC BC A B ABC BC A C D A B C A BC B B C C D 9 4 9 9 + 4 = 4 4 + 9 = 7 7 4 9 獉獉 3 9- BC = BC A B = A B C = C A BC A BC 9-3 9-9-3 a A B = BC b A B > BC c d e C f C e 8
4 9-4 AA B BC C 5 + = 60 AA B 3 A AB AA B 60 AA = A B = AB BC C 4 C CB CC B 60 CC = C B = BC 3 4 60 A BC = ABC 9-4 A B = AB BC = BC A BC ABC 5 = 6 CC B = 60 5 + = 60 A BC ABC 5 9-5 AB = AC AD = AE BD = EC BD = EC ABD ACE AB = AC AD = AE 9-5 3 = 4 BAE = ACD ABE ACD B = C = AC = AB AD = AE BD = EC BE = CD ABE ACD AD = AE, = C = B AD = AE, CAD BAE AAS, CD = BE CD - DE = BE - DE BD = EC 6 AF BE G 9-6 BAC = 90 AB = AC AD BC D DH = DF 9-6 BAC = 90 AB = AC AD BC ABC = BAD = DAC = 45 9
BD = AD = CD AG BE 4 + 7 = 90 DH = DF Rt BHD 5 = 6 BH = AF 3 = 4 Rt AFD BD = AD 5 = 6 7 = 6 4 + 7 = 90 4 + 6 = 90 AD BC 4 + 6 = 90 BH = AF ABH CAF BAD = ABD = DAC = C AB = AC = AFC = BHA 3 = 4 AD BC AG BE 5 = 7 AD = CD DH = DF AH = CF ABH CAF AD BC 4 + 6 = 90 AF BE 3 + 6 = 90 3 = 4 7 9-7 P ABC PA+ PB + PC < AB + BC + CA PA< AB PB < BC PC < CA 9-7 AB + BC + CA< PA+ PB + PC AB < PA BC < PB CA < PC AB + BC + CA < PA + PB + PC PA PB PC AB < PA + PB BC < PB + PC CA < PC + PA PA + PB + PC < AB + BC + CA PA PB PC AB BC CA PA PB + PC < AB + AC 30 BP AC D ABC BD < AB + AD PDC PC < PD + CD, BD + PC < AB + AD + PD + CD PB + PC < AB + AC PA+ PC < AB + BC PA+ PB < BC + CA, PA+ PB + PC < AB + BC + CA
PA+ PB + PC < AB + BC + CA 3 8 9-8 OA= OB AC = BD OE AOB OE AOB OAE OBE OCE ODE 9-8 AEC BED AOD BOC AEC BED 3 = 4 AEC BED 3 = 4 OC = OD OE = OE OCE ODE OA= OB AC = BD, OC = OD AOB = AOB OA= OB, AOD BOC SAS, 3 = 4 5 = 6 AC = BD, AEC BED AAS, CE = DE 3 = 4 OC = OD, OCE ODE SAS = Ⅰ 獉獉 獉獉 9 9-9 ACB = 45 CE AB E BD AC D AD = DH 9-9 3
ABD HCD AD = DH AD 3 4 CH AB BD CD A 5 Rt BDC ACB = 45, DBC = 45 = ACB, BD = CD Rt ABD 4 + A= 90 3 + A= 90, 4 = 3 = 90 =, ABD HCD ASA, AD = DH Ⅱ 0 9-0 AB > AC AD BAC BD > DC PB > PC 3 AB + PC > PB + AC AD 9-0 AB AC' = AC DC' DC 9- a 3 PC' PC 9- a 3 9- AB > AC AB AC' = AC DC' 9- a 4 = 5 AD = AD, ADC' ADC SAS, = 3 DC' = DC > 3 > B, > B BC' D BD > DC'
, BD > DC 9- a AB > AC AB AC' = AC PC' 9- ABC > 5, > 5 PC' = PC > = 3 3 > 4 4 > ABC BC' P PB > PC' PB > PC 3 BC' P 9- a C' B > PB - PC' C' B = AB - AC' = AB - AC, AB - AC > PB - PC' AB + PC > PB + AC AB AC' = AC DC' AB DC 9- a AC B' AB' = AB DB' AC BD 9- b a 3 9- b b 9-3 AC > AB AD < E EB EBD ACD E BE ABE BE > AB E < 9-3 AC E EB EC ABEC 3 9-4 a BO CO ABC ACB MON BC MN = BM + CN 33
9-4 b CO BO ACB ABC MNO BC MN = BM - CN MON BC 9-4, = 3 =, = 3, MO = BM NO = CN, MN = BM + CN MNO BC, = 3 =, = 3, MO = BM NO = CN, MN = BM - CN BMO CNO BO CO MN BMO CNO 9-5 D AB Ⅰ Ⅱ ACB = 90 D AB 9-5 Ⅲ Ⅳ CD = AB DB = CD AD = CD ACB = 90 CD = AB 45 60 34
80 9-6 3 9-6 AB CD AE DE BAD ADC E BC AD = AB + DC AB CD B 90 AE > AB AED = 90 AD > AE > AB AD = AB + DC AD AF = AB AD > AB 9-7 AFE ABE SAS 5 = B DEF DEC AB CD B + C = 80 5 + 6 = 80 5 = B 6 = C DEF DEC AAS FD = DC AD = AB + DC AD AD 9-7 AB DC AE AD AF = AB E EA EA EB AEF = AEB AED = 90 > AEB EF AD F + 3 = 90 + 3 = 90 3 = 4 AEB AEF DEF DEC ASA AB = AF DC = DF DE AED = 90 9-8 AE DC E ADE E DE ASA AD = DE = DC + CE EE = AE ECE EBA ASA CE = AB 9-8 9-9 EF AB 9-9 EF AD F α = 7 = 8 AF = EF AED = 90 EF = AD F AD 35
0 EF = AB + DC AD = AB + DC 3 4 α a 9-0 ABC = AC BAC = α AD = a AD BC D 9-0 9- EAF = α AG EAF AG AD = a 3 D MN AG AE AF B C ABC AD BC BAC 9-, AB = AC BD AD BC D AD = a 3 BAC = α, ABC 9- α 9-0 GAF = α 9- AD AD = a DP AG AF C 3 CD B BD = CD AB ABC 9-36
AD BC BD = CD, AB = AC AD BAC AD = a 3 AD BAC, BAC = DAC = α = α, ABC MN EAF B C ADC Rt ADC AD DC DAC = α AD = a 3 9 A 3 B 4 4 C 4 D 7 33 5 A C B 3 D A B C D 4 A ABC AB A' B' C' A' B' C > C' B C D 30 5 60 60 3 37
4 A C 4 B 4 D 4 6 3 60 4 A 34 B 3 C D 3 7 8 9 Rt ABC AC BC ACE BCF CE BF 0 ABC D BC < AC > AB 9-3 9-4 AC BC AE = AC BD = BC ECD = 45 9-3 9-4 9-5 = BD AE AB = BC E = C 3 9-6 CE CF ACB EF BC AC D DE = DF 9-5 9-6 38 4 ABCD AC BD O O A B C D 9-7 5 9-8 BAD < 80 ABCD A B C D
9-7 9-8 6 AB = CD AD = BC OB = OD 9-9 OE = OF 7 9-30 D AB CD = BD AB = BC A= 30 9-9 9-30 8 9-3 ABC DE AB DF AC MDN 9 9-3 BD = AE AB = BC = CA EC = ED 9-3 9-3 0 3 39
() 0-0- 0-0- 40
3 0-3 0-3 4 0-4 0-4 4
5 0-5 0-5 0-3 45 0-6 0-6 3 4
3 4 0-7 CA' AB AB A 5 0-8 5 6 0-7 0-8 3 0-9 CE BD BD 6 4 0-0 0-9 0-0 0- ABC ADF DBE FEC EFD ADEF BDFE CFDE Ⅰ 0-7 43
Ⅱ Ⅰ 8 9 0- ABCD E F AC BEDF ABE CDF SAS BFC DEA BE 瓛 DF BF 瓛 DE BEDF 0-3 BD AC O OB = OD OE = OA - AE = OC - CF = OF BEDF 0-0-3 0-4 ABCD AE = BF = CG = DH EFGH ABCD A= B = 90 AB = AD AE = DH, AB - AE = AD - DH AH = BE AE = BF, HAE EBF SAS, HE = EF = 0-4 + 3 = 90, 4 = 80 - + 3 = 80 - + 3 = 90 5 = 6 = 90, EFGH 44
AC BD O OE OF OG OH 0-5 ABCD OA= OC OB = OD AC = BD, OA= OB = OD DAB = ABC = CDA= 90, 4 = 5 = 6 AE = BF = DH AOE BOF DOH SAS, = = 3 OE = OF = OH OE = OG FOH EOG, EG = OE + OG = OF + OH = FH ABCD AOD = 90, EOH = + AOH = 3 + AOH = ACD = 90 EG FH OE = OG OF = OH 0-5, EFGH 3 EG FH 0-6 EG FH ABCD O EFGH ABCD OC = AC = BD = OB 3 = BCD = ABC = 4 + 5 = 90 0-6 EG FH + 5 = 90, = BOE, OE = OF COF ASA OE = OF = OG = OH EG = FH EG FH, EFGH ABCD OC = AC = BD = OB 3 = BCD = ABC = 4 + 5 = 90 EG FH + 5 = 90 =, BOE COF ASA, EB = FC EB = FC = GD = HA 45
3 3 EFGH 90 90 4 0-7 ABCD AF CE F AF CD G DG = DE CDE ADG ABCD ADC = CDE = 90 3 + E = 90 AFC = 90 3 + = 90 = = E 3 AD = DC 0-7 ABCD ADC = EDC = 90 5 0-8 ABCD BC AD A= D AB = CD AB A' C CA' D = A= D CD = CA' = AB BB' CC' 0-9 ABB' DCC' AAS AB = CD 0-8 AB DC E 0-0 A = D AE = DE = BE = CE AB = CD 0-9 0-0 6 ACD 0- ABCD BC AD AC = BD AB = CD CE BD = BD = AC = E = ADB DBA SAS AB = CD 0- BB' CC' Rt ACC' Rt DBB' HL CAD = BDA ACD DBA SAS AB = CD 0-46
0-0- 5 6 7 0-3 E F ABCD BD CE = CF AB AD ABCD G E AB FB 0-3 B AF GE ABF GE EC AF CF AE AECF AC EF O OA= OC OE = OF BE = DF OB = OE + BE = OF + DF = OD AD 8 0-4 E F AC BD CD AB E F EF > CD - AB E F AC BD BC AD AB CD AC BD AC AB 0-4 AC BC G AD EG FG GE = AB GF = DC 9 EF > GF - GE = DC - AB = DC - AB a b e f a b 0-5 ABCD BC AD = a AD = b AC = f BD = e 0-6 0-5 ACE D B ABCD 0-6 ACE AE = b + a AC = f CE = e AE ED = a 3 E CD CB 瓛 ED AB 0-6 47
ABCD 0-7 BD BC 瓛 DE, DBCE, BC = ED = a BD = CE = e AD = AE - ED = a + b - a = b 3 AC = f 4 CB AD = a b = AD, ABCD ABCD 0-7 ACE B 0 A B C D A C B D 3 3 4 A 34 C 4 B D 3 4 A B C D 5 A C B D 6 7 8 9 48 0 a cm a cm 0-8 E F ABCD BD BF = DE AECF
0-9 ABCD BE DF CBD ADB BC = BD BF = CE 0-8 0-9 3 P Q ABCD AD CD BQ PBC BP = PD + CD CQ = QD 4 5 0-30 ABCD E BD DG CE G DG AC F OE = OF 6 0-3 ABCD B BC AD F CE BF E CE = CD 0-30 0-3 7 8 9 0 0-3 BC AD < AD E F AC BD EF BC = AD - BC 0-33 E F AB CD AC > BD OG > OH 0-3 3 4 0-34 CD AB D E F G AC CB AB DEF = FGB 49
0-33 0-34 5 0-35 B C D A B G H A F E G H CF DE CD = FE EAH = DBH 6 ABCD BC = 3 AD = 7 BD AC O BD = 5 BO 7 0-35 8 9 30 3 3 0 cm 8 cm 6 cm 33 6 cm 0 cm 50
(! - a - b - l l' l' l - 3-3 ABC BCD ABE DEC - -3 S = a + b h a b h -4 5
-4 S = bh b h -5 BE CF AD AD E F ABE DCF ABCD BCFE AD BE = bh 3-6 -5-6 3 4 4 30 60 : 槡 3: : 槡 3: 30 60 90 ABC A= 30 B = 60 C = 90 a b = 槡 3 b c = 槡 3 a c = 45 : : 槡 : : 槡 45 45 90 3 槡 3 槡 3 3 槡 3 槡 3 6 4 5
4 槡 -7 D E F AB BC CD S DEF = 8 S ABC - a -7 S DEF = S DEC = ( ) S BDC = ( ABC ) [ ] S = 8 S ABC -8 cm cm 4 3-9 AB = AC BD AC D CE AB E BD = CE S ABC =, BD AC = CE AB AB = AC, BD = CE BD AC S ABC = CE AB -8 ABC AB AC -9 4-0 EFGH H ABCD 3 - -3 FF EG FF GH F EF FG O - S EOF = S F OG EFGH EF H ABCD F F EH F F AB F HF -0-5 53