Đáp án: A=1/7
Giải thích các bước giải:
$\begin{array}{l}
\frac{{{x^2} + {y^2}}}{{xy}} = \frac{{25}}{{12}}\\
\Rightarrow \frac{{{x^2} + 2xy + {y^2} - 2xy}}{{xy}} = \frac{{25}}{{12}}\\
\Rightarrow \frac{{{{\left( {x + y} \right)}^2} - 2xy}}{{xy}} = \frac{{25}}{{12}}\\
\Rightarrow \frac{{{{\left( {x + y} \right)}^2}}}{{xy}} - 2 = \frac{{25}}{{12}}\\
\Rightarrow \frac{{{{\left( {x + y} \right)}^2}}}{{xy}} = \frac{{49}}{{12}}\\
\Rightarrow {\left( {x + y} \right)^2} = \frac{{49}}{{12}}.xy\\
\Rightarrow x + y = - \frac{{7\sqrt {xy} }}{{2\sqrt 3 }}\left( {do:x < y < 0} \right)\left( 1 \right)\\
\frac{{{x^2} + {y^2}}}{{xy}} = \frac{{25}}{{12}}\\
\Rightarrow \frac{{{{\left( {x - y} \right)}^2} + 2xy}}{{xy}} = \frac{{25}}{{12}}\\
\Rightarrow \frac{{{{\left( {x - y} \right)}^2}}}{{xy}} + 2 = \frac{{25}}{{12}}\\
\Rightarrow \frac{{{{\left( {x - y} \right)}^2}}}{{xy}} = \frac{1}{{12}}\\
\Rightarrow {\left( {x - y} \right)^2} = \frac{{xy}}{{12}}\\
\Rightarrow x - y = - \frac{{\sqrt {xy} }}{{2\sqrt 3 }}\\
\Rightarrow A = \frac{{x - y}}{{x + y}} = \frac{{\frac{{ - \sqrt {xy} }}{{2\sqrt 3 }}}}{{ - \frac{{7\sqrt {xy} }}{{2\sqrt 3 }}}} = \frac{1}{7}
\end{array}$
