Đáp án:
\[\left[ \begin{array}{l}
x = y = 10\\
\left\{ \begin{array}{l}
x = - 10\\
y = - 12
\end{array} \right.\\
\left\{ \begin{array}{l}
x = - 10\\
y = 30
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 10\\
y = - 32
\end{array} \right.
\end{array} \right.\]
Giải thích các bước giải:
\(\begin{array}{l}
3{x^2} - {y^2} - 2xy - 2x - 2y + 40 = 0\\
\Leftrightarrow 4{x^2} - \left( {{x^2} + {y^2} + 1 + 2xy + 2x + 2y} \right) + 41 = 0\\
\Leftrightarrow {\left( {2x} \right)^2} - {\left( {x + y + 1} \right)^2} = - 41\\
\Leftrightarrow {\left( {x + y + 1} \right)^2} - {\left( {2x} \right)^2} = 41\\
\Leftrightarrow \left( {3x + y + 1} \right)\left( { - x + y + 1} \right) = 41\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
3x + y + 1 = 41\\
- x + y + 1 = 1
\end{array} \right.\\
\left\{ \begin{array}{l}
3x + y + 1 = - 41\\
- x + y + 1 = - 1
\end{array} \right.\\
\left\{ \begin{array}{l}
3x + y + 1 = 1\\
- x + y + 1 = 41
\end{array} \right.\\
\left\{ \begin{array}{l}
3x + y + 1 = - 1\\
- x + y + 1 = - 41
\end{array} \right.
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = y = 10\\
\left\{ \begin{array}{l}
x = - 10\\
y = - 12
\end{array} \right.\\
\left\{ \begin{array}{l}
x = - 10\\
y = 30
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 10\\
y = - 32
\end{array} \right.
\end{array} \right.
\end{array}\)
