Question

(n+4)chia hết cho(n+1)

(n²+n)chia hết cho(n²+1)

Answer 1

Ta có: n + 4 ⋮ n + 1

⇒ n + 1 + 3 ⋮ n + 1

⇒ 3 ⋮ n +1

⇒ n + 1 ∈ { 1;-1;3;-3 }

⇒ n ∈ { 0;-2;2;-4}

Vậy n ∈ { 0;-2;2;-4}

Answer 2

a, \(n+4⋮n+1\)

Mà \(n+1⋮n+1\)

\(\Leftrightarrow3⋮n+1\)

\(\Leftrightarrow n+1\inƯ\left(3\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}n+1=1\\n+1=3\\n+1=-1\\n+1=-3\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}n=0\\n=2\\n=-2\\n=-4\end{matrix}\right.\)

Vậy ...

Answer 3

n+4= n+1+3

để (n+4) \(⋮\)(n+1)

=> 3\(⋮\)(n+1)

=> n+1 \(\in\)Ư(3)=\(\left\{-1,+1,-3,+3\right\}\)

=> n\(\in\)\(\left\{-2,0,-4,2\right\}\)