Question

Tìm Min:

E=\(4xy+6y-5x^2-y^2+1\)

Answer 1

- Sửa đề: Tìm max.

\(E=4xy+6y-5x^2-y^2+1\)

\(=-5\left(x^2-2.\dfrac{2}{5}xy+\dfrac{4}{25}y^2\right)-\dfrac{1}{5}\left(y^2-30y+225\right)+46\)

\(=-5\left(x-\dfrac{2}{5}y\right)-\dfrac{1}{5}\left(y-15\right)^2+46\le46\)

 - Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x-\dfrac{2}{5}y=0\\y-15=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=6\\y=15\end{matrix}\right.\)

- Vậy \(MaxE=46\)