\(\Leftrightarrow\left\{{}\begin{matrix}x^2+xy+y^2=13\\\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)=91\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x^2+xy+y^2=13\\x^2-xy+y^2=7\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y\right)^2-xy=13\\\left(x+y\right)^2-3xy=7\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y\right)^2=16\\xy=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x+y=4\\x+y=-4\end{matrix}\right.\\xy=3\end{matrix}\right.\)
TH1: \(\left\{{}\begin{matrix}x+y=4\\xy=3\end{matrix}\right.\) \(\Rightarrow\left(x;y\right)=\left(3;1\right);\left(1;3\right)\)
TH2: \(\left\{{}\begin{matrix}x+y=-4\\xy=3\end{matrix}\right.\) \(\Rightarrow\left(x;y\right)=\left(-3;-1\right);\left(-1;-3\right)\)
