Question

Tìm GTNN 

 F=\(2x^2+8xy+11y^2-4x-2y+18\)

Answer 1

\(F=2x^2+8xy+11y^2-4x-2y+18\)

\(=2\left[x^2+2x\left(2y-1\right)+\left(2y-1\right)^2\right]+3\left(y^2+2y+1\right)+13\)

\(=2\left(x+2y-1\right)^2+3\left(y+1\right)^2+13\ge13\)

\(minF=13\Leftrightarrow\) \(\left\{{}\begin{matrix}x=3\\y=-1\end{matrix}\right.\)