\(x^3-7x+6=0\Leftrightarrow x^3-x-6x+6=0\Leftrightarrow x\left(x^2-1\right)-6\left(x-1\right)=0\Leftrightarrow x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)=0\Leftrightarrow\left(x-1\right)\left(x\left(x+1\right)-6\right)=0\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x\left(x+1\right)-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x^2+x-6=0\left(''\right)\end{matrix}\right.\) Giả TH (''): \(x^2+x-6=0\Leftrightarrow x^2+3x-2x-6=0\Leftrightarrow x\left(x+3\right)-2\left(x+3\right)=0\Leftrightarrow\left(x-2\right)\left(x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\) Vậy \(S=\left\{2;-3;1\right\}\)
\(\Leftrightarrow x^3-x-6x+6=0\)
\(\Leftrightarrow x\left(x-1\right)\left(x+1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+x-6\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\\x=3\end{matrix}\right.\)
