a/ \(x^3-7x+6=0\Leftrightarrow x^3-x-6x+6=0\)
\(\Leftrightarrow x\left(x^2-1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^2+x\right)\left(x-1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+x-6\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2+3x-2x-6\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x\left(x+3\right)-2\left(x+3\right)\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x+3\right)=0\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-3\end{matrix}\right.\)
b/ \(x^2+y^2-6x+6y+18=0\)
\(\Leftrightarrow x^2-6x+9+y^2+6y+9=0\)
\(\Leftrightarrow\left(x-3\right)^2+\left(y+3\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-3=0\\y+3=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=3\\y=-3\end{matrix}\right.\)
