\(\left\{{}\begin{matrix}\left(x^2+2x\right)\left(y^2+2y\right)=9\\\left(x^2+2x\right)+\left(y^2+2y\right)=6\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[6-\left(y^2+2y\right)\right]\left(y^2+2y\right)=9\\\left(x^2+2x\right)=6-\left(y^2+2y\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(y^2+2y\right)^2-6\left(y^2+2y\right)+9=0\\\left(x^2+2x\right)=6-\left(y^2+2y\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(y^2+2y-3\right)^2=0\\\left(x^2+2x\right)=6-\left(y^2+2y\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y^2+2y-3=0\\\left(x^2+2x\right)=6-\left(y^2+2y\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}y=1\\y=-3\end{matrix}\right.\\\left(x^2+2x\right)=6-\left(y^2+2y\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}y=1\\x^2+2x=6-y^2-2y\end{matrix}\right.\\\left\{{}\begin{matrix}y=-3\\x^2+2x=6-y^2-2y\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}y=1\\x^2+2x-3=0\end{matrix}\right.\\\left\{{}\begin{matrix}y=-3\\x^2+2x-3=0\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}y=1\\\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\end{matrix}\right.\\\left\{{}\begin{matrix}y=-3\\\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\end{matrix}\right.\end{matrix}\right.\)
vậy \(S=\left\{\left(1;1\right),\left(-3;1\right),\left(1;-3\right),\left(-3;-3\right)\right\}\)
