Đáp án:
$\begin{array}{l}
A = - 2{x^2} + 4xy - 4{y^2} - 2x - 1\\
= - {x^2} + 4xy - 4{y^2} - {x^2} - 2x - 1\\
= - {\left( {x - 2y} \right)^2} - {\left( {x + 1} \right)^2} \le 0\\
\Leftrightarrow GTLN:A = 0\,khi:\left\{ \begin{array}{l}
x = - 1\\
y = \dfrac{1}{2}
\end{array} \right.
\end{array}$