KöMaL 2014 C1203

Show that if $x$, $y$ and $z$ are rational numbers such that $x$+$y \ne z$, $z \ne$0, and ($a$-1)$^2 x$+($a$-1)$^2 y$- ( $a^2$-1 ) $z$=0, then $a$ is also a rational number.