Question

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

Answer 1

\(\Leftrightarrow\left(x^2-2x+2-1\right)^2=0\\ \Leftrightarrow\left[\left(x-1\right)^2\right]^2=0\\ \Leftrightarrow x-1=0\Leftrightarrow x=1\)

Answer 2

\(\Rightarrow\left(x^2-2x+2-1\right)^2=0\Rightarrow\left(x^2-2x+1\right)^2=0\Rightarrow\left[\left(x-1\right)^2\right]^2=0\Rightarrow x-1=0\Rightarrow x=1\)