\(1.x^3-7x-6=0\)
\(\Leftrightarrow\left(x+1\right)\left(x^2-x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x^2-x-6=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\\left(x+2\right)\left(x-3\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-2\\x=3\end{matrix}\right.\)
\(2.x^3-3x^2+2=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-2x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x^2-2x-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=1\pm\sqrt{3}\end{matrix}\right.\)
\(3.3x^2-x+2=0\)
\(\Leftrightarrow\left(x+1\right)\left(3x^2-3x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\3x^2-3x+2=0\left(\Delta=9-24=-15< 0\Rightarrow x\in\varnothing\right)\end{matrix}\right.\)
\(\Leftrightarrow x=-1\)
