用配方法解下列方程:x^2-2根号2x+1=0

Question

如题所述

Answer 1

x^2-2√2x=-1
x^2-2√2x+2=-1+2
(x-√2)^2=1
x-√2=±1
x=√2-1，x=√2+1

Answer 2

x^2-2根号2x+1=0
x^2-2根号2x=-1
x^2-2根号2x+2=-1 +2
(x-根号2)^2=1
x-根号2=±1
x1=根号2-1
x2=根号2+1

Answer 3

x^2-2根号2x+1=0
x^2-2根号2x+2-1=0
x^2-2根号2x+2=1
（x-根号2）^2=1
x-根号2=±1
x1=根号2+1 x2=根号2-1

Answer 4

x^2-2√2x+1=0
x^2-2√2x+2-1=0
x^2-2√2x+(√2)^2-1=0
(x-√2)^2-1=0
(x-√2-1)(x-√2+1)=0
x=√2+1或x=√2-1