Question

[Cậu Bé Bí Ẩn]

n +4 chia hết cho n + 2

Hướng dẫn mình nha !

Answer 1

[Nguyễn Huy Tú]

Giải:

Ta có:

\(n+4⋮n+2\)

\(\Rightarrow\left(n+2\right)+2⋮n+2\)

\(\Rightarrow2⋮n+2\)

\(\Rightarrow n+2\in\left\{1;-1;2;-2\right\}\)

+) \(n+2=1\Rightarrow n=-1\)

+) \(n+2=-1\Rightarrow n=-3\)

+) \(n+2=2\Rightarrow n=0\)

+) \(n+2=-2\Rightarrow n=-4\)

Vậy \(n\in\left\{-1;-3;0;-4\right\}\)

Answer 2

[Lê Yên Hạnh]

\(n+4⋮n+2\)

\(\Rightarrow\left(n+2\right)+2⋮n+2\)

Do \(n+2⋮n+2\) nên để \(n+4⋮n+2\) thì \(2⋮n+2\)

\(\Rightarrow n+2\inƯ\left(2\right)\)

\(\Rightarrow n+2\in\left\{1;2\right\}\)

\(\Rightarrow n\in\left\{-1;0\right\}\)