1. Ta có:
$x^2-y^2=17$
$\Leftrightarrow (x-y)(x+y)=17$
$\Leftrightarrow \left[\begin{array}{l}\left\{\begin{array}{l}x-y=1\\x+y=17\end{array}\right.\\\left\{\begin{array}{l}x-y=-1\\x+y=-17\end{array}\right.\\\left\{\begin{array}{l}x-y=17\\x+y=1\end{array}\right.\\\left\{\begin{array}{l}x-y=-17\\x+y=-1\end{array}\right.\end{array}\right.$
$\Leftrightarrow \left[\begin{array}{l}\left\{\begin{array}{l}x=9\\y=8\end{array}\right.\\\left\{\begin{array}{l}x=-9\\y=-8\end{array}\right.\\\left\{\begin{array}{l}x=9\\y=-8\end{array}\right.\\\left\{\begin{array}{l}x=-9\\y=8\end{array}\right.\end{array}\right.$