Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
{x^2} - 2xy + 3{y^2} = 9\\
{x^2} - 4xy + 5{y^2} = 5
\end{array} \right. \to \left\{ \begin{array}{l}
3xy - 2{y^2} = 4\\
{x^2} - 2xy + 3{y^2} = 9
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y(3x - 2y) = 4\\
{x^2} - 2xy + 3{y^2} = 9
\end{array} \right. \to \left\{ \begin{array}{l}
x = (\frac{4}{y} + 2y):3 = \frac{{4 + 2{y^2}}}{{3y}}\\
\frac{{16 + 16{y^2} + 4{y^4}}}{{9{y^2}}} - 2.\frac{{4 + 2{y^2}}}{3} + 3{y^2} = 9(*)
\end{array} \right.\\
\left( * \right) \to 16 + 16{y^2} + 4{y^4} - 24{y^2} - 12{y^4} + 27{y^4} = 81{y^2}\\
\to 19{y^4} - 89{y^2} + 16 = 0 \to \left[ \begin{array}{l}
{y^2} = \frac{{89 + 3\sqrt {745} }}{{38}}\\
{y^2} = \frac{{89 + 3\sqrt {745} }}{{38}}
\end{array} \right.\\
\to \left[ \begin{array}{l}
y = \pm \sqrt {\frac{{89 + 3\sqrt {745} }}{{38}}} \\
y = \pm \sqrt {\frac{{89 - 3\sqrt {745} }}{{38}}}
\end{array} \right. \to \left[ \begin{array}{l}
x = \pm \frac{{4 + 2{{\left( {\sqrt {\frac{{89 + 3\sqrt {745} }}{{38}}} } \right)}^2}}}{{3\left( {\sqrt {\frac{{89 + 3\sqrt {745} }}{{38}}} } \right)}}\\
x = \pm \frac{{4 + 2{{\left( {\sqrt {\frac{{89 - 3\sqrt {745} }}{{38}}} } \right)}^2}}}{{3\left( {\sqrt {\frac{{89 - 3\sqrt {745} }}{{38}}} } \right)}}
\end{array} \right.
\end{array}\)
