2^x+2^y+2^​z=1024

^​but 1024=512+256+256

so \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x=9\\y=8\\z=8\end{matrix}\right.\\\left\{{}\begin{matrix}x=8\\y=9\\z=8\end{matrix}\right.\\\left\{{}\begin{matrix}x=8\\y=8\\z=9\end{matrix}\right.\end{matrix}\right.\)