Question

如何用因式分解法解下列方程

①（3x-1)²=(3x-1)(4x-3)
②(x-5)(x+2)=8
③x(x-√3)+(x-√3)²=0
④2x²-4x=70
⑤(x+2)²=4x+8
⑥（7x-1)²=(2x+4)²

Answer 1

1.(3x-1)²=(3x-1)(4x-3)
(3x-1)²-(3x-1)(4x-3)=0
(3x-1)(3x-1-4x+3)=0
(3x-1)(2-x)=0
x=1/3 or 2
2.(x-5)(x+2)=8
x²-3x-10=8
x²-3x-18=0
(x-6)(x+3)=0
x=6 or x=-3
3.x(x-√3)+(x-√3)²=0
(x-√3)(x+x-√3)=0
x=√3 or x=√3/2
4.2x²-4x=70
x²-2x-35=0
(x-7)(x+5)=0
x=7 or x=-5
5.(x+2)²=4x+8
(x+2)²=4(x+2)
(x+2)(x+2-4)=0
x=-2 or x=2
6.(7x-1)²=(2x+4)²
(7x-1)²-(2x+4)²=0
(7x-1+2x+4)(7x-1-2x-4)=0
(9x+3)(5x-5)=0
x=-3 or x=1

Answer 2

2.x²-3x-10=8
x²-3x-18=0
(x-6)(x+3)=o
x1=6,x2=-3