ĐKXĐ: `x≥1` và `x≤-1`
`\sqrt{x^2-2x+1}=x^2-1`
`⇔\sqrt{(x-1)^2}=(x-1)(x+1)`
`⇔|x-1|=(x-1)(x+1)`
Với `x≥0`
`⇒|x-1|=x-1`
`⇒x-1=(x-1)(x+1)`
`⇔(x-1)(x+1)-(x-1)`
`⇔(x-1)(x+1-1)=0`
`⇔(x-1)x=0`
`⇔`\(\left[ \begin{array}{l}x=1\\x=0(KTM)\end{array} \right.\)
Với `x<0 `
`⇒|x-1|=1-x`
`⇔1-x=(x-1)(x+1)`
`⇔(x-1)(x+1)+(x-1)=0`
`⇔(x-1)(x+1+1)=0`
`⇔(x-1)(x+2)=0`
`⇔`\(\left[ \begin{array}{l}x=1\\x=-2\end{array} \right.\)
