\(2x^2-2xy+2y^2-6x-6y+18=0\)
\(\Leftrightarrow x^2+x^2-2xy+y^2+y^2-6x-6y+9+9=0\)
\(\Leftrightarrow\left(x^2-2xy+y^2\right)+\left(x^2-6x+9\right)+\left(y^2-6y+9\right)=0\)
\(\Leftrightarrow\left(x-y\right)^2+\left(x-3\right)^2+\left(y-3\right)^2=0\)
Mà \(\left(x-y\right)^2\ge0;\left(y-3\right)^2\ge0;\left(x-3\right)^2\ge0\)
\(\Rightarrow\hept{\begin{cases}x-y=0\\y-3=0\\x-3=0\end{cases}}\Leftrightarrow z=y=3\)
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