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