\(x^2+11y^2-6xy+4y+2=0\)
\(\Leftrightarrow\left(x^2-6xy+9y^2\right)+\left(2y^2+4y+2\right)=0\)
\(\Leftrightarrow\left(x-3y\right)^2+2\left(y^2+2y+1\right)=0\)
\(\Leftrightarrow\left(x-3y\right)^2+2\left(y+1\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(x-3y\right)^2=0\\2\left(y+1\right)^2=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x-3y=0\\y+1=0\end{cases}}\)\(\Leftrightarrow\hept{\begin{cases}x-3\left(-1\right)=0\\y=-1\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=-3\\y=-1\end{cases}}\)
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