Đáp án:
Giải thích các bước giải:
$\begin{array}{l}
{x^2} + 2{y^2} + 2xy + 7x + 7y + 10 = 0\\
\Leftrightarrow \left( {{x^2} + 2xy + {y^2}} \right) + \left( {7x + 7y} \right) + 10 + {y^2} = 0\\
\Leftrightarrow {\left( {x + y} \right)^2} + 7\left( {x + y} \right) + 10 = - {y^2}\\
Vi\, - {y^2} \le 0,\forall y\,nen:\\
{\left( {x + y} \right)^2} + 7\left( {x + y} \right) + 10 \le 0 \Leftrightarrow - 5 \le x + y \le - 2\\
\Rightarrow - 5 + 1 \le x + y + 1 \le - 2 + 1\\
\Leftrightarrow - 4 \le A \le - 1
\end{array}$
$\begin{array}{l}
\min A = - 4\,khi\,\left\{ \begin{array}{l}
y = 0\\
x + y = - 5
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = - 5\\
y = 0
\end{array} \right.\\
\max A = - 1\,khi\,\left\{ \begin{array}{l}
y = 0\\
x + y = - 2
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = - 2\\
y = 0
\end{array} \right.
\end{array}$
