Question

Answer 1

\(2A=-2x^2-4y^2+4xy-6x+12\)

\(=-\left(x^2-4xy+4y^2\right)-\left(x^2+6x+9\right)+21\)

\(=-\left(x-2y\right)^2-\left(x+3\right)^2+21\le21\)

\(\Rightarrow A\le\dfrac{21}{2}\)

\(A_{max}=\dfrac{21}{2}\) khi \(\left\{{}\begin{matrix}x=-3\\y=-\dfrac{3}{2}\end{matrix}\right.\)