Đáp án:
$\begin{array}{l}
\left\{ \begin{array}{l}
\frac{{{y^2} - {x^2}}}{3} = \frac{{{x^2} - {y^2}}}{5}\\
{x^{10}}.{y^{10}} = 1024 \Rightarrow {\left( {x.y} \right)^{10}} = {2^{10}} \Rightarrow xy = 2
\end{array} \right.\\
\Rightarrow 5\left( {{y^2} - {x^2}} \right) - 3\left( {{x^2} - {y^2}} \right) = 0\\
\Rightarrow 5\left( {{y^2} - {x^2}} \right) + 3\left( {{y^2} - {x^2}} \right) = 0\\
\Rightarrow {y^2} - {x^2} = 0\\
\Rightarrow \left( {y - x} \right)\left( {y + x} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
x = y\\
x = - y
\end{array} \right.\\
+ )Khi\,x = y \Rightarrow x.x = 2 \Rightarrow {x^2} = 2 \Rightarrow x = \pm \sqrt 2 \\
+ )\,Khi\,x = - y \Rightarrow x.\left( { - x} \right) = 2\left( {loai} \right)\\
Vậy\,x = y = \pm \sqrt 2
\end{array}$
