5 mũ x + 5 mũ y = 3250

Giải thích các bước giải:

 `5^x+5^y=3250`

`=>5^3(5^(x-3)+5^(y-3))=3250`

`=>5^(x-3)+5^(y-3)=26`

Do `26` không chia hết cho `5`

`=>`\(\left[ \begin{array}{l}5^{x-3}=1\\5^{y-3}=1\end{array} \right.\) `=>`\(\left[ \begin{array}{l}\left\{\begin{matrix}5^{x-3}=1\\5^{y-3}=25\end{matrix}\right.\\\left\{\begin{matrix}5^{x-3}=25\\5^{y-3}=1\end{matrix}\right.\end{array} \right.\)

`=>`\(\left[ \begin{array}{l}\left\{\begin{matrix}x-3=0\\y-3=2\end{matrix}\right.\\\left\{\begin{matrix}x-3=2\\y-3=0\end{matrix}\right.\end{array} \right.\) `=>`\(\left[ \begin{array}{l}\left\{\begin{matrix}x=3\\y=5\end{matrix}\right.\\\left\{\begin{matrix}x=5\\y=3\end{matrix}\right.\end{array} \right.\)

    Vậy `(x;y) in {(3;5);(5;3)}.`