a, \(E=-4x^2+4x-3\)
\(=-\left(4x^2+4x+1-4\right)\)
\(=-\left[\left(2x+1\right)^2-4\right]=-\left(2x+1\right)^2+4\le4\)
Dấu " = " khi \(-\left(2x+1\right)^2=0\Leftrightarrow x=\dfrac{-1}{2}\)
Vậy \(MAX_E=4\) khi \(x=\dfrac{-1}{2}\)
b, \(F=13-2x^2+4y+4xy-3y^2\)
\(=17-\left(2x^2-4xy+2y^2\right)-\left(y^2-4y+4\right)\)
\(=17-2\left(x-y\right)^2-\left(y-2\right)^2\le17\)
Dấu " = " khi \(\left\{{}\begin{matrix}2\left(x-y\right)^2=0\\\left(y-2\right)^2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=y\\y=2\end{matrix}\right.\Leftrightarrow x=y=2\)
Vậy \(MAX_F=17\) khi x = y = 2
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