Question

tìm x, y sao cho B= \(-x^2+2xy-4y^2+2x+10y-8\)

đạt GTLN

Answer 1

\(6B=-6x^2+12xy-24y^2+12x+60y-48\)

\(=\left(-4x^2+12xy-9y^2\right)+\left(-2x^2+12x\right)+\left(-15y^2+60y\right)-48\)

\(=-\left(2x-3y\right)^2-2\left(x^2-6x+9\right)-15\left(y^2-4y+4\right)+30\)

\(=-\left(2x-3y\right)^2-2\left(x-3\right)^2-15\left(y-2\right)^2+30\le30\)

Dấu "=" xảy ra khi \(2x-3y=0;\text{ }x-3=0;\text{ }y-2=0\Leftrightarrow x=3;\text{ }y=2\)

Vậy GTLN của B là \(\frac{30}{8}=5\) tại x = 3; y = 2.