\(\Leftrightarrow\left\{{}\begin{matrix}x^3y+2x^2y^2+xy^3+x^3y^2+x^2y^3=30\\x^2y+xy^2+xy+x+y=11\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}xy\left(x^2+2xy+y^2\right)+x^2y^2\left(x+y\right)=30\\xy\left(x+y\right)+\left(xy+x+y\right)=30\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}xy\left(x+y\right)^2+x^2y^2\left(x+y\right)=30\\xy\left(x+y\right)+\left(xy+x+y\right)=11\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}xy\left(x+y\right)\left(xy+x+y\right)=30\\xy\left(x+y\right)+\left(xy+x+y\right)=11\end{matrix}\right.\)
Theo Viet đảo, \(xy\left(x+y\right)\) và \(xy+x+y\) là nghiệm của:
\(t^2-11t+30=0\Rightarrow\left[{}\begin{matrix}t=6\\t=5\end{matrix}\right.\)
TH1: \(\left\{{}\begin{matrix}xy\left(x+y\right)=6\\xy+x+y=5\end{matrix}\right.\)
Theo Viet đảo, \(xy\) và \(x+y\) là nghiệm của: \(u^2-5u+6=0\Rightarrow\left[{}\begin{matrix}u=2\\u=3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+y=2\\xy=3\end{matrix}\right.\\\left\{{}\begin{matrix}x+y=3\\xy=2\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow\left(x;y\right)=\left(1;2\right);\left(2;1\right)\)
TH2: \(\left\{{}\begin{matrix}xy\left(x+y\right)=5\\xy+x+y=6\end{matrix}\right.\) ..........
