Đáp án:
\(n{\displaystyle\in}\)`{0;2}`
Giải thích các bước giải:
\(\dfrac{5n+14}{n+2}=\dfrac{5n+10+4}{n+2}=\dfrac{5.(n+2)+4}{n+2}=5+\dfrac{4}{n+2}\)
\(5n+14\,\, \vdots\,\,n+2\Rightarrow n+2{\displaystyle\in}Ư(5n+14)\Leftrightarrow n+2{\displaystyle\in}Ư(4)\)
\(\Rightarrow n+2{\displaystyle\in}\)`{1;2;4}`
\(n+2=1\Rightarrow n=-1\)
\(n+2=2\Rightarrow n=0\)
\(n+2=4\Rightarrow n=2\)
Mà \(n{\displaystyle\in}N\)
Vậy \(n{\displaystyle\in}\)`{0;2}`