a , \(5x^2+9y^2-12xy-6x+9=0\)
\(\Leftrightarrow25x^2+45y^2-60xy-30x+45=0\)
\(\Leftrightarrow\left(5x\right)^2-2.5.\left(6y+3\right)+\left(6y+3\right)^2+9y^2-36y+36=0\)
\(\Leftrightarrow\left(5x-6y-3\right)^2+9\left(y^2-4y+4\right)=0\)
\(\Leftrightarrow\left(5x-6y-3\right)^2+9\left(y-2\right)^2=0\)
Vì \(\left\{{}\begin{matrix}\left(5x-6y-3\right)^2\ge0\\9\left(y-2\right)^2\ge0\end{matrix}\right.\Rightarrow\left(5x-6y-3\right)^2+9\left(y-2\right)^2\ge0\)
Dấu ''='' xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}5x-6y-3=0\\y-2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\)
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