\(\sqrt{x^4-2x^2+1}=x-1\\ \left(\sqrt{x^4-2x^2+1}\right)=\left(x-1\right)^2\\ x^4-2x^2+1-x^2+2x-1=0\\ x^4-3x^2+2x=0\\ x^4-x^2-2x^2+2x=0\\ x^2\left(x-1\right)-2x\left(x-1\right)=0\\ \left(x^2-2x\right)\left(x-1\right)=0\\ \left[{}\begin{matrix}x-1=0\\x\left(x-2\right)=0\end{matrix}\right.=>x=1;x=0;x=2\)