a.
\(5x^2+y^2+4xy-6x=-9\)
\(\Leftrightarrow\left(4x^2+4xy+y^2\right)+\left(x^2-6x+9\right)=0\)
\(\Leftrightarrow\left(2x+y\right)^2+\left(x-3\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x+y=0\\x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-6\end{matrix}\right.\)
b.
\(x^2+26y^2+2y+1=10xy\)
\(\Leftrightarrow\left(x^2-10xy+25y^2\right)+\left(y^2+2y+1\right)=0\)
\(\Leftrightarrow\left(x-5y\right)^2+\left(y+1\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-5y=0\\y+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-1\\x=-5\end{matrix}\right.\)
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