Question

Tìm giá trị lớn nhất:

B = \(-4x^2\) - \(5y^2\) + 8xy + 10y +12

Answer 1

\(B=-4x^2-5y^2+8xy+10y+12\)

\(=-4x^2+8xy-4y^2-y^2+10y-25+37\)

\(=-\left(2x-2y\right)^2-\left(y-5\right)^2+37< =37\forall x,y\)

Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}2x-2y=0\\y-5=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=5\\x=y=5\end{matrix}\right.\)