Question

tìm n∈z

6n - 1⋮ 3n + 5

giúp mình nhé mình đang cần gấp

Answer 1

Ta có :

\(6n-1⋮3n+5\)

Mà \(3n+5⋮3n+5\)

\(\Leftrightarrow\left\{{}\begin{matrix}6n-1⋮3n+5\\6n+10⋮3n+5\end{matrix}\right.\)

\(\Leftrightarrow11⋮3n+5\)

Vì \(n\in Z\Leftrightarrow3n+5\in Z;3n+5\inƯ\left(11\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}3n+5=1\\3n+5=11\\3n+5=-1\\3n+5=-11\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=\dfrac{-4}{3}\left(loại\right)\\n=2\\n=-2\\n=\dfrac{-16}{3}\left(loại\right)\end{matrix}\right.\)

Vậy ..