\(\left\{{}\begin{matrix}2x^2+y=3y^2-2\\2y^2+x=3x^2-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2\left(x-y\right)\left(x+y\right)-\left(x-y\right)=-3\left(x-y\right)\left(x+y\right)\\2x^2+y=3y^2-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5\left(x-y\right)\left(x+y\right)-\left(x-y\right)=0\\2x^2+y=3y^2-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5\left(x-y\right)\left(x+y-1\right)=0\\2x^2+y=3y^2-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}x=y\\x=1-y\end{matrix}\right.\\2x^2+y=3y^2-2\end{matrix}\right.\)
TH1: x=y
\(\Rightarrow\left[{}\begin{matrix}x=y=2\\x=y=-1\end{matrix}\right.\)
TH2: x=1-y
\(\Rightarrow\left[{}\begin{matrix}y=1\\y=-4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)
Vậy............
