\(y^4+y^2+x^2-8y-4x+2xy+7=0\)
\(\Leftrightarrow\left(y^4-4y+3\right)+\left(x^2+y^2+4+2xy-4x-4y\right)=0\)
\(\Leftrightarrow\left(y-1\right)^2\left[\left(y+1\right)^2+2\right]+\left(x+y-2\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}y-1=0\\x+y-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)
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