Question

用因式分解法解x^2=2x （x+1)^2-(2x-3)^2=0 x^2-6x+8=0 4(x+3)^2=25(x-2)^2 (1+根号2)x^2-(1-根号2）x=0

Answer 1

解
x²=2x
x²-2x=0
x(x-2)=0
x=0或x=2

(x+1)²-(2x-3)²=0
(x+1+2x-3)(x+1-2x+3)=0
(3x-2)(-x+4)=0
∴x=2/3或x=4

x²-6x+8=0
(x-4)(x-2)=0
∴x=4或x=2

4(x+3)³=25(x-2)²
4(x+3)²-25(x-2)²=0
[2(x+3)+5(x-2)][2(x+3)-5(x-2)]=0
(7x-3)(-3x+16)=0
∴x=3/7或x=16/3

(1+√2)x²-(1-√2)x=0
x[(1+√2)x-(1-√2)]=0
∴x=0
或x=(1-√2)/(1+√2)=(1-√2)²/(1-2)=-(1-2√2+2)=-3+2√2