\(x^4-16x^2+32x-16=0\)

\(\Leftrightarrow x^4-16\left(x^2-2x+1\right)=0\)

\(\Leftrightarrow x^4-16\left(x-1\right)^2=0\)

\(\Leftrightarrow x^4-\left(4\left(x-1\right)\right)^2=0\)

\(\Leftrightarrow\left(x^2-4\left(x-1\right)\right).\left(x^2+4\left(x-1\right)\right)=0\)

\(\Leftrightarrow\left(x^2-4x+4\right).\left(x^2+4x-4\right)=0\)

\(\Leftrightarrow\left(x-2\right)^2.\left(x^2+4x-4\right)=0\)

\(\Leftrightarrow\)\(\left(x-2\right)^2=0\) hoặc \(x^2+4x-4=0\)

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

\(2\)) \(x^2+4x-4=0\Leftrightarrow x^2+4x+4-8=0\)

\(\Leftrightarrow\left(x+2\right)^2=8\)

\(\Leftrightarrow x+2=\sqrt{8}\) hoặc \(x+2=-\sqrt{8}\)

\(\Leftrightarrow x=\sqrt{8}-2\) \(x=-\sqrt{8}-2\)

Vậy tập nghiệm của phương trình là \(S=\left\{2;\sqrt{8}-2;-\sqrt{8}-2\right\}\)