Đáp án:
\(\left[ \begin{array}{l}
y = - 2\\
y = 2
\end{array} \right. \to \left[ \begin{array}{l}
x = - 3\\
x = 3
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
DK:x \ne 0;y \ne 0\\
\left\{ \begin{array}{l}
\dfrac{x}{y} - \dfrac{y}{x} = \dfrac{5}{6}\\
{x^2} - {y^2} = 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{{{x^2} - {y^2}}}{{xy}} = \dfrac{5}{6}\\
{x^2} - {y^2} = 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\dfrac{5}{{xy}} = \dfrac{5}{6}\\
{x^2} - {y^2} = 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
xy = 6\\
{x^2} - {y^2} = 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{6}{y}\\
\dfrac{{36}}{{{y^2}}} - {y^2} = 5\left( 1 \right)
\end{array} \right.\\
\left( 1 \right) \to 36 - {y^4} = 5{y^2}\\
\to - {y^4} - 5{y^2} + 36 = 0\\
\to \left[ \begin{array}{l}
{y^2} = 4\\
{y^2} = - 9\left( l \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
y = - 2\\
y = 2
\end{array} \right.
\end{array}\)
\( \to \left[ \begin{array}{l}
x = - 3\\
x = 3
\end{array} \right.\)
