PHNG TRNH CHA CN THC1. PHNG PHP LU THA
Dng 1 : Phng trnh Dng 2: Phng trnh Dng 3: Phng trnh
A 0( B 0) A= B A = B B 0 A=B 2 Tng qut: A = B
2k
B 0 A=B 2k A = B
+) A +
B =
C
A 0 0 B A +B + 2 AB= C
(chuyn v dng 2)
3 3 3 3 +) A + B = C A + B + 3 A.B
(
3
A + 3 B = C (1)
)
v ta s dng php th : 3 A + 3 B = C ta c phng trnh : A + B + 3 3
A.B.C = C (2) Dng 4:3
A = B A = B3 ;
2 k +1
A = B A = B2 k +1
Ch : - Phng trnh (2) l phng trnh h qu ca ph tr (1). - Php bnh
phng 2 v ca mt phng trnh m khng c iu kin cho 2 v khng m l mt php
bin i h qu. Sau khi tm c nghim ta phi th li. Gii cc phng trnh sau:
1) 4) 10) 13) 16) 18) 3) ( x 3) x 2 4 = x 2 9 6) 9)3
x2 4x + 6 = x + 43x 2 9 x + 1 = x 23
2) 5) 8) 11) 14) 17)
x 2 2x + 4 = 2 xx 2 3x + 2 3 x = 0
3x 2 9 x + 1 = x 2 x + 1 + 3 x 1 = 3 5x x 1 x 2 = x 3 x + 2 3 x
= 5 2x x2 + 9 x2 7 = 2
7) 3x 3 3x 1 = 5 x + 5 + 3 x + 6 = 3 2 x + 11 x + 3 7 x = 2x 8 y
14 12 y = 0
4 1 x = 2 x3
x +1 + 3 x + 2 + 3 x + 3 = 0 5 x 1 3x 2 x 1 = 0 19) x +1 = x + 9
2
12) 15)
3x2 + 6x + 16+ x2 + 2x = 2 x2 + 2x + 4
x 2 + 3x + 2 + x 2 + 6 x + 5 = 2 x 2 + 9 x + 7
20)
(20) x + 3 + 3 x + 1 = 2 x + 2 x + 2 Nhn xt : Nu phng trnh :
phng trnh v dng
f ( x ) + g ( x ) = h ( x ) + k ( x ) M c : f ( x ) + h ( x ) =
g ( x ) + k ( x ) , th ta bin i f ( x ) h ( x ) = k ( x ) g ( x )
sau bnh phng ,gii phng trnh h qu
x3 + 1 (21) + x + 1 = x2 x + 1 + x + 3 x+3 Nhn xt :
Nu phng trnh :
f ( x ) + g ( x ) = h ( x ) + k ( x ) M c : f ( x ) .h ( x ) = k
( x ) .g ( x ) th ta bin i2. PHNG PHP T N PH
f ( x ) h ( x ) = k ( x ) g ( x ) sau bnh phng ,gii phng trnh h
qu Dng 1: Cc phng trnh c dng : A.B + A.B + = 0 , t t = A.B A.B = t
2 . f ( x ) + . f ( x ) + = 0 , t t = f ( x) f ( x) = t 2 .( x a )(
x b) + ( x a )x b x b + = 0 t t = ( x a ) ( x a)( x b) = t 2 xa
xa
Ch : Nu khng c iu kin cho t, sau khi tm c x th phi th li Bi 1.
Gii cc phng trnh sau: 7) 5 x 2 + 10 x + 1 = 7 x 2 2 x 1) ( x + 1)(
x + 4) = 5 x 2 + 5 x + 284) x 2 4 x + 2 = 2 x 2 4 x + 52)
( x 3) 2 + 3x 22 =
x 2 3x + 7
3) x( x + 5) = 23 x 2 + 5 x 2 2
5) 4 (4 x)(2 + x) = x 2 2 x 12 6) (4 + x)(6 x) = x 2 2 x 12 Bi
2. Tm m phng trnh sau c nghim? a) (1 + 2 x)(3 x) = 2 x 2 5 x + 3 +
m b) x 2 + 2 x + 4 ( 3 x )( x + 1) = m 3 Bi 3. Cho phng trnh: x 2 +
2 x + 4 (3 x)( x + 1) = m 2 a. Gii phng trnh khi m = 12 b. Tm m
phng trnh c nghim? x+1 Bi 4. Cho phng trnh: (x 3)(x + 1) + 4(x 3) =
m (3) x 3 a. Gii phng trnh vi m = -3 b. Tm m phng trnh c nghim?
