Giải thích các bước giải:
ĐKXĐ: \(\left\{ \begin{array}{l}
x \ne 0\\
y \ne 0
\end{array} \right.\)
Ta có:
\(\begin{array}{l}
\left\{ \begin{array}{l}
\left( {x + y} \right)\left( {1 + \frac{1}{{xy}}} \right) = 5\,\,\,\,\,\,\,\,\,\,\left( 1 \right)\\
{\left( {x + y} \right)^2}\left( {1 + \frac{1}{{{x^2}{y^2}}}} \right) = 49\,\,\,\left( 2 \right)
\end{array} \right.\\
\left( 1 \right) \Leftrightarrow x + y = \frac{5}{{1 + \frac{1}{{xy}}}}\\
\left( 2 \right) \Leftrightarrow \frac{{25}}{{{{\left( {1 + \frac{1}{{xy}}} \right)}^2}}}\left( {1 + \frac{1}{{{x^2}{y^2}}}} \right) = 49\\
\Leftrightarrow 25 + \frac{{25}}{{{x^2}{y^2}}} = 49\left( {1 + \frac{2}{{xy}} + \frac{1}{{{x^2}{y^2}}}} \right)\\
\Leftrightarrow \frac{{24}}{{{x^2}{y^2}}} + \frac{{98}}{{xy}} + 24 = 0\\
\Leftrightarrow \frac{1}{{xy}} = .....
\end{array}\)
