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a) HPT
$\Leftrightarrow \left\{ \begin{array}{l} 7(2 x^{2}-4xy +y^{2} )=-7\\ 3 x^{2}+2xy +2y^{2} =7\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} 7(2 x^{2}-4xy +y^{2} )+3 x^{2}+2xy +2y^{2}=0\\ 3 x^{2}+2xy +2y^{2} =7\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} 17x^{2}-26xy +9y^{2}=0\\ 3 x^{2}+2xy +2y^{2} =7\end{array} \right.$
$\Leftrightarrow \left\{ \begin{array}{l} (17x-9y)(x-y)=0\\ 3 x^{2}+2xy +2y^{2} =7\end{array} \right.$
$\Leftrightarrow \left[ {\begin{matrix} \begin{cases} x=y\\ 3 x^{2}+2xy +2y^{2} =7 \end{cases}\\\\ \begin{cases}17x=9y\\ 3 x^{2}+2xy +2y^{2} =7 \end{cases}\end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix} x=y=\pm1\\\\ \begin{cases}x= \pm \dfrac{9}{\sqrt{161}}\\ y= \pm \dfrac{17}{\sqrt{161}}
\end{cases}\end{matrix}} \right.$
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