Ta có: \(3n+2⋮n-1\)
\(\Leftrightarrow3n-3+5⋮n-1\)
Mà: \(3n-3⋮n-1\)
\(\Rightarrow5⋮n-1\Leftrightarrow n-1\inƯ_{\left(5\right)}\left\{-5;-1;1;5\right\}\)
\(\Leftrightarrow\left[{}\begin{matrix}n-1=-5\\n-1=-1\\n-1=1\\n-1=5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}n=-4\\n=0\\n=2\\n=6\end{matrix}\right.\)
Vậy:\(n=-4;0;2;6\)
_Chúc bạn học tốt_
Ta có:
\(3n+2⋮n-1\)
\(\Rightarrow\left(3n-3\right)+5⋮n-1\)
\(\Rightarrow3\left(n-1\right)+5⋮n-1\)
\(\Rightarrow5⋮n-1\)
\(\Rightarrow n-1\in U\left(5\right)=\left\{-1;1-5;5\right\}\)
+)\(n-1=-1\Rightarrow n=0\)
+)\(n-1=1\Rightarrow n=2\)
+)\(n-1=-5\Rightarrow n=-4\)
+)\(n-1=5\Rightarrow n=6\)
Vậy \(n=0\) hoặc \(n=-4\) hoặc \(n=2\) hoặc \(n=6\)
