a) \(2x^2+4y^2-4xy-12y+4x+10=0\)
\(\Leftrightarrow2\left(x^2+y^2+1-2xy+2x-2y\right)\left(y^2-4y+4\right)+2=0\)
\(\Leftrightarrow2\left[\left(x-y\right)^2+2\left(x-y\right)+1\right]+2\left(y-2\right)^2=0\)
\(\Leftrightarrow2\left(x-y+1\right)^2+2\left(y-2\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-y+1=0\\y-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)
b) \(4x^2+10y^2+12xy-28x-48y+58=0\)
\(\Leftrightarrow\left(4x^2+9y^2+49+12xy-28x-42y\right)+\left(y^2-6y+9\right)=0\)
\(\Leftrightarrow\left[\left(2x+3y\right)^2-14\left(2x+3y\right)+49\right]+\left(y-3\right)^2=0\)
\(\Leftrightarrow\left(2x-3y+7\right)^2+\left(y-3\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x-3y+7=0\\y-3=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=3\end{matrix}\right.\)
