Answer:
\(n+2\) là ước của \(2n+14\)
\(\Rightarrow2n+14⋮n+2\)
\(\Rightarrow2\left(n+2\right)+10⋮n+2\)
Mà \(2\left(n+2\right)⋮n+2\)
\(\Rightarrow10⋮n+2\)
\(\Rightarrow n+2\inƯ\left(10\right)=\left\{\pm1;\pm2;\pm5;\pm10\right\}\)
\(\Rightarrow n\in=\left\{-1;-3;0;-4;3;-7;8;-12\right\}\)
Ta có :
\(n+2⋮n+2\)
\(\Rightarrow2n+4⋮n+2\)
\(\Leftrightarrow2n+4-2n-14⋮n+2\)
\(\Leftrightarrow-10⋮n+2\)
\(\Rightarrow n+2\in\text{Ư}\left(-10\right)=\left\{\pm1;\pm2;\pm5;\pm10\right\}\)
\(\Rightarrow n\in\left\{-1;-3;0;-4;3;-7;8;-12\right\}\)
Mà n là số tự nhiên
\(\Rightarrow n\in\left\{3\right\}\)
