a ) \(x^3+3x^2+3x+2=0\)

\(\Leftrightarrow x^3+3x^2+3x+1+1=0\)

\(\Leftrightarrow\left(x+1\right)^3+1=0\)

\(\Leftrightarrow\left(x+1\right)^3=-1\)

\(\Leftrightarrow x+1=-1\)

\(\Leftrightarrow x=-2\)

Vậy \(x=-2\)

b ) \(x^4-2x^3+2x-1=0\)

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

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

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

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

\(\Leftrightarrow\left(x-1\right)^3\left(x+1\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)

Vậy \(\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)