Question

用分解因式法解方程①4x(2-x)=3(2-x)②3（x-1）x=2-2x③4(x+1)^2=9(2x-1)^2④（x-1）^2=1-x^2

Answer 1

①4x(2-x)=3(2-x)
(4x-3)(2-x)=0
x1=3/4 x2=2
②3（x-1）x=2-2x
3(x-1)x=2(1-x)
(x-1)(3x+2)=0
x1=1 x2=-2/3
③4(x+1)^2=9(2x-1)^2
[2(x+1)-3(2x-1)][2(x+1)+3(2x-1)]=0
(-4x+5)(8x-1)=0
x1=5/4 x2=1/8
④（x-1）^2=1-x^2
(x-1)^2=(1+x)(1-x)
(x-1)^2+(1+x)(x-1)=0
(x-1)(x-1+1+x)=0
2x(x-1)=0
x1=0 x2=1

Answer 2

①4x(2-x)=3(2-x) 4x(2-x)-3(2-x)=0 (4x-3)(2-x)=0 x=3/4 x=2
②3（x-1）x=2-2x 3(x-1)x+2(x-1)=0 (3x+1)(x-1)=0 x=-1/3 x=1
③4(x+1)^2=9(2x-1)^2 4(x+1)^2-9(2x-1)^2=0 [2(x+1)+3(2x-1)][2(x+1)-3(2x-1)]=0 (8x-1)(-4x+1)=0 x=1/8 x=1/4
④（x-1）^2=1-x^2 (x-1)^2-1+x^2=0 (x-1-1)(x-1+1)+x^2=0 x(x-2)+x^2=0 x(x-2+x)=0 2x(x-1)=0 x=0 x=1