Question

min

C=x^2-6x+5y^2+4xy-10y+20

Answer 1

\(C=x^2-6x+5y^2+4xy-10y+20=\left[x^2+2x\left(2y-3\right)+\left(2y-3\right)^2\right]+\left(y^2+2y+1\right)+10=\left(x+2y-3\right)^2+\left(y+1\right)^2+10\ge10\)

\(minC=10\Leftrightarrow\)\(\left\{{}\begin{matrix}x=5\\y=-1\end{matrix}\right.\)