Question

Tìm GTLN:

C=\(-x^2\)+2xy-\(^{ }4y^2\)+2x+10y-3

Answer 1

\(C=-x^2+2xy-4y^2+2x+10y-3\)

\(=-\left(x^2-2xy+y^2\right)+3y^2+2x+10y-3\)

\(=-\left(x^2-2xy+y^2\right)+2x-2y+12y-3y^2-3\)

\(=-\left(x^2-2xy+y^2\right)+2\left(x-y\right)-3y^2+12y-3\)

\(=-\left(x^2-2xy+y^2\right)+2\left(x-y\right)-\left(3y^2-12y+12\right)+9\)

\(=-\left(x^2-2xy+y^2\right)+2\left(x-y\right)-3.\left(y^2-4y+4\right)+9\)

Xét \(-\left(x^2-2xy+y^2\right)+2\left(x-y\right)-3.\left(y^2-4y+4\right)+9\le9\)

\(\Rightarrow Max_C=9\)