Question

用因式分解法解方程 (x-5)²=2(5-x)

①(x-5)²=2(5-x) ②（3x-2）²-（x+1）²=0

Answer 1

(x-5)²=2(5-x)

x²-10x+25=10-2x
x²-8x+15=0
(x-3)(x-5)=0
x1=3,x2=5

（3x-2）²-（x+1）²=0

9x²-12x+4-x²-2x-1=0
8x²-14x+3=0
(4x-1)(2x-3)=0
x1=1/4
x2=3/2

Answer 2

(x-5)²=2(5-x)
(x-5)^2+2(x-5)=0
(x-5)(x-5+2)=0
x1=5, x2=3

②（3x-2）²-（x+1）²=0
[(3x-2)+(x+1)][(3x-2)-(x+1)]=0
(4x-1)(2x-3)=0
x1=1/4, x2=3/2

追问

不是(x-5)²-2(5-x)=0吗