Ta có
$\left\{\begin{array}{l}x^4-y^4=544\\6x^3+27x^2+10y^3-75y^2=-54x-250y\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x^4+81=y^4+625\\12x^3+54x^2+108x=-20y^3+150y^2-500y\end{array}\right.$
$\Leftrightarrow \left\{\begin{array}{l}x^4-y^4=544\\(x+3)^4=(y-5)^4\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}\left\{\begin{array}{l}x^4-y^4=544\\x+3=y-5\end{array}\right.\\\left\{\begin{array}{l}x^4-y^4=544\\x+3=5-y\end{array}\right.\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}\left\{\begin{array}{l}x=-5\\y=3\end{array}\right.\\\left\{\begin{array}{l}x=5\\y=-3\end{array}\right.\end{array}\right.$