Question

ayudaaaaaaaaaa!!!!!!!!!!

Answer 1

$\overline{xyz}-\overline{zyx}=\overline{mn4}\\ \\ (100x+10y+z)-(100z+10y+x)=\overline{mn4}\\ \\ 99x-99z=\overline{mn4}\\ \\ 99(x-z)=\overline{mn4}\\ \\ \texttt{de esto se deduce: }\\ \\ \begin{cases} m+n+4=9\°\\ m+4=n \end{cases}\\ \\ 2(m+4)=9\°\to m+4=9\°\to m=5\to n=9\to \overline{mn4}=594\\ \texttt{Entonces: }x-z=6\\ \\ x+y+z=20\\ 6+2z+y=20\\ 2z+y=14 ~\cdots (x\ \textgreater \ z\ \textgreater \ 0)\\ \\ (x,y,z)\in\{(7,12,1),(8,10,2),(9,8,3),(10,6,4),\cdots\}\\ \\ \texttt{Por consiguiente }(x,y,z)=(9,8,3)$

$\textbf{Respuesta: }x\cdot y\cdot z = 9\times 8\times 3 = 216$