a) \(\Leftrightarrow4x^2+2y^2+4xy-20x-8y+26=0\)
\(\Leftrightarrow4x^2+4x\left(y-5\right)+\left(y-5\right)^2-\left(y-5\right)^2+2y^2-8y+26=0\)
\(\Leftrightarrow\left(2x+y-5\right)^2+y^2+2y+1=0\)
\(\Leftrightarrow\left(2x+y-5\right)^2+\left(y+1\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x+y-5=0\\y+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-1\end{matrix}\right.\) ( TM )
b) \(\Leftrightarrow\left(x^2-4x+4\right)+\left(y^2+6y+9\right)+\left(z^2-2z+1\right)=0\)
\(\Leftrightarrow\left(x-2\right)^2+\left(y+3\right)^2+\left(z-1\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-2=0\\y+3=0\\z-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-3\\z=1\end{matrix}\right.\) ( TM )
c) \(\Leftrightarrow\left(x^2+y^2+z^2+2xy+2yz+2xz\right)+\left(x^2+2x+1\right)+\left(z^2-4z+4\right)=0\)
\(\Leftrightarrow\left(x+y+z\right)^2+\left(x+1\right)^2+\left(z-2\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y+z=0\\x+1=0\\z-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=-1\\z=2\end{matrix}\right.\) ( TM )
