\(5x^2+9y^2-12xy-6x+9=0\)
\(\Rightarrow\left(4x^2+9y^2-12xy\right)+\left(x^2-6x+9\right)=0\)
\(\Rightarrow\left(2x-3y\right)^2+\left(x-3\right)^2=0\)
\(\Rightarrow\hept{\begin{cases}2x-3y=0\\x-3=0\end{cases}\Rightarrow\hept{\begin{cases}2x=3y\\x=3\end{cases}\Rightarrow}\hept{\begin{cases}y=2\\x=3\end{cases}}}\)
\(5x^2+9y^2-12xy-6x+9=0\)
<=> \(\left(4x^2-12xy+9y^2\right)+\left(x^2-6x+9\right)=0\)
<=> \(\left(2x-3y\right)^2+\left(x-3\right)^2=0\)
<=> \(\hept{\begin{cases}2x-3y=0\\x-3=0\end{cases}}\)
<=> \(\hept{\begin{cases}y=2\\x=3\end{cases}}\)
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