\(x^3-3x+2=0\)
\(\Leftrightarrow x^3-x-2x+2=0\)
\(\Leftrightarrow x\left(x^2-1\right)-2\left(x-1\right)=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)-2\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+x-2\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x^2-x+2x-2\right]=0\)
\(\Leftrightarrow\left(x-1\right)\left[x\left(x-1\right)+2\left(x-1\right)\right]=0\)
\(\Leftrightarrow\left(x-1\right)^2\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x+2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)
\(x^3-3x+2=0\)
\(\Leftrightarrow x^3-x^2+x^2-x-2x+2=0\)
\(\Leftrightarrow x^2\left(x-1\right)+x\left(x-1\right)-2\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^2+x-2\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^2-x+2x-2\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[x\left(x-1\right)+2\left(x-1\right)\right]\left(x-1\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(x-1\right)^2=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=1\end{matrix}\right.\)
Vậy \(S=\left\{-2;1\right\}\)
