\(T=x^2+2xy+2y^2-2x-2y-2\)
\(=\left(x^2+2xy-2x+y^2-2y+1\right)+y^2-3\)
\(=\left(x+y-1\right)^2+y^2-3\ge-3\)
Dấu "=" xảy ra khi \(\left\{\begin{matrix}\left(x+y-1\right)^2=0\\y^2=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x+y-1=0\\y=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=1\\y=0\end{matrix}\right.\)
Vậy \(Min_T=-3\) khi \(\left\{\begin{matrix}x=1\\y=0\end{matrix}\right.\)
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