Question

用因式分解法解下列方程 1. x(x-1/2)=x 2. 1/2(x-2)^2+x-2=0 3. 9(2x+3)^2-4(2x-5)^2=0

Answer 1

1. x(x-1/2)=x
x(x-1/2)-x=0
x(x-1/2-1)=0
x(x-3/2)=0
x=0或x=3/2

2. 1/2(x-2)^2+x-2=0
1/2(x-2)(x-2+2)=0
1/2x(x-2)=0
x=0或x=2

3. 9(2x+3)^2-4(2x-5)^2=0
[3(2x+3)+2(2x-5)][3(2x+3)-2(2x-5)]=0
(10x-1)(2x+19)=0
x=1/10或x=-19/2

Answer 2

1.x(x-1/2)=x
x(x-1/2)-x=0
x(x-1/2-1)=0
x=0 or x=3/2
2.1/2(x-2)^2+x-2=0
(x-2)^2+2(x-2)=0
(x-2)(x-2+2)=0
x=2 or x=0
3. 9(2x+3)^2-4(2x-5)^2=0
[3(2x+3)-2(2x-5)] [3(2x+3)+2(2x-5)] =0
(6x+9-4x+10) (6x+9+4x-10) =0
(2x+19) (10x-1) =0
x=-19/2 or x=1/10

Answer 3

x(x-1/2)=x
x(x-1/2)-x=0
x（x-1/2-1）=0
x=0
x=3/2

1/2(x-2)^2+x-2=0

（x-2）【1/2（x_2）+1）】=0

9(2x+3)^2-4(2x-5)^2=0
【3（(2x+3)-2(2x-5)】[3(2x+3)+2(2x-5)]=0