Cho phương trình \(\left\{ \begin{array}{l}2{...

A

- Hướng dẫn giải

\(\begin{array}{l}
\left\{ {\begin{array}{*{20}{l}}
{2{x^2} + {y^2} + 3xy = 12}\\
{2{{(x + y)}^2} - {y^2} = 14}
\end{array}} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
2{x^2} + {y^2} + 3xy = 12\\
2{x^2} + 4xy + 2{y^2} - {y^2} = 14
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
xy = 2\\
2{x^2} + {y^2} + 3xy = 12
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
y = \frac{2}{x}\\
2{x^2} + \frac{4}{{{x^2}}} + 6 = 12
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
y = \frac{2}{x}\\
2{x^4} - 6{x^2} + 4 = 0
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
y = \frac{2}{x}\\
{x^2} = 1 \vee {x^2} = 2
\end{array} \right.\\
 \Leftrightarrow \left\{ \begin{array}{l}
y =  \pm 2,y =  \pm \sqrt 2 \\
x =  \pm 1,x =  \pm \sqrt 2 
\end{array} \right.
\end{array}\)

Đáp án A.