问题 解答题

用因式分解法解下列方程:

(1)(4x-1)(5x+7)=0.

(2)3x(x-1)=2-2x.

(3)(2x+3)2=4(2x+3).

(4)2(x-3)2=x2-9.

答案

(1))(4x-1)(5x+7)=0,

4x-1=0,5x+7=0,

x1=

1
4
,x2=-
7
5

(2)3x(x-1)=2-2x,

3x(x-1)+2(x-1)=0,

(x-1)(3x+2)=0,

x-1=0,3x+2=0,

x1=1,x2=-

2
3

(3)(2x+3)2=4(2x+3),

(2x+3)2-4(2x+3)=0,

(2x+3)(2x+3-4)=0,

2x+3=0,2x+3-4=0,

x1=-

3
2
,x2=
1
2

(4)2(x-3)2=x2-9,

2(x-3)2-(x+3)(x-3)=0,

(x-3)[2(x-3)-(x+3)]=0,

x-3=0,2(x-3)-(x+3)=0,

x1=3,x2=9.

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