a: \(=-\left(x^2-4x+y^2-6y-2022\right)\)
\(=-\left(x^2-4x+4+y^2-6y+9-2035\right)\)
\(=-\left(x-2\right)^2-\left(y-3\right)^2+2035\le2035\)
Dấu '=' xảy ra khi x=2 và y=3
b: \(=-\left(x^2+4y^2+2x-8y-11\right)\)
\(=-\left(x^2+2x+1+4y^2-8y+4-16\right)\)
\(=-\left(x+1\right)^2-\left(2y-2\right)^2+16\le16\)
Dấu '=' xảy ra khi x=-1 và y=1
\(C=-x^2-2y^2+2xy-4y+101\)
\(=-\left(x^2-2xy+y^2\right)-\left(y^2+4y+4\right)+105\)
\(=-\left(x-y\right)^2-\left(y+2\right)^2+105\le105\)
Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}\left(x-y\right)^2=0\\\left(y+2\right)^2=0\end{matrix}\right.\Leftrightarrow x=y=-2\)
Vậy \(MaxC=105\)
