\(C=x^2+2y^2+2xy-2y\)
\(=\left(x^2+2xy+y^2\right)+\left(y^2-2y+1\right)-1\)
\(=\left(x+y\right)^2+\left(y-1\right)^2-1\ge-1\forall x;y\)
Dấu " = " xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x+y=0\\y-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-y\\y=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=1\end{matrix}\right.\)
Vậy Min C là : \(-1\Leftrightarrow x=-1;y=1\)
\(E=7-x^2-y^2-2\left(x+y\right)\)
\(=7-\left(x^2+2x+1\right)-\left(y^2+2y+1\right)+2\)
\(=9-\left(x+1\right)^2-\left(y+1\right)^2\le9\forall x;y\)
Dấu " = " xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x+1=0\\y+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1\\y=-1\end{matrix}\right.\)
Vậy Max E là : \(9\Leftrightarrow x=y=-1\)
