Question

Answer 1

Ta có: \(3^{m+n}+243=3^{m+3}+3^{n+2}\)

=>\(3^{m+n}-3^{m+3}=3^{n+2}-243\)

=>\(3^{m}\left(3^{n}-^{}3^3\right)=3^2\left(3^{n}-3^3\right)\)

=>\(\left(3^{n}-3^3\right)\left(3^{m}-3^2\right)=0\)

=>\(\begin{cases}3^{n}-3^3=0\\ 3^{m}-3^2=0\end{cases}\Rightarrow\begin{cases}n=3\\ m=2\end{cases}\)