Question

Tìm m,n biết :

3^m-1 *5ⁿ⁺¹ = 45^m+n

Answer 1

\(3^{m-1}.5^{n+1}=45^{m+n}\)

\(\Leftrightarrow3^{m-1}.5^{n+1}=\left(3^2.5\right)^{m+n}\)

\(\Leftrightarrow3^{m-1}.5^{n+1}=3^{2.\left(m+n\right)}.5^{m+n}\)

Khi đó ta có: \(\left\{{}\begin{matrix}m-1=2\left(m+n\right)\\n+1=m+n\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m-1=2m+2n\\n+1=m+n\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m=-1-n\\m=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m=1\\n=-2\end{matrix}\right.\)

Vậy \(m=1;n=-2\)