Question

Tìm giá trị nhỏ nhất : \(E=7-x^2-y^2-2\left(x+y\right)\)

Answer 1

\(E=7-x^2-y^2-2\left(x+y\right)\)

\(=7-x^2-y^2-2x-2y\)

\(=7-\left(x^2+2x+1\right)-\left(y^2+2y+1\right)+2\)

\(=9-\left(x+1\right)^2-\left(y+1\right)^2\le9\forall x;y\)

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 : \(9\Leftrightarrow x=y=-1\)