\(E=5-x^2+2x-4y^2-4y\)
\(=-\left(x^2-2x+1\right)-\left(4y^2+4y+1\right)+7\)
\(=-\left(x-1\right)^2-\left(2y+1\right)^2+7\)
Ta có : \(-\left(x-1\right)^2\le0\) ; \(-\left(2y+1\right)^2\le0\) với mọi x,y
\(\Rightarrow-\left(x-1\right)^2-\left(2y+1\right)^2+7\le7\)
hay E ≤ 7
Dấu = xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}\left(x-1\right)^2=0\\\left(2y+1\right)^2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-\dfrac{1}{2}\end{matrix}\right.\)
Vậy \(Max_E=7\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=-\dfrac{1}{2}\end{matrix}\right.\)
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