Question

Tìm số tự nhiên n,biết 6n +17 chia hết cho n+2

Answer 1

\(\left(6n+17\right)⋮\left(n+2\right)\)

\(\Rightarrow\left(6n+12+5\right)⋮\left(n+2\right)\)

\(\Rightarrow5⋮\left(n+2\right)\)

\(\Rightarrow n+2\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\)

\(\Rightarrow n\in\left\{-7;-3;-1;3\right\}\)

\(\text{Mà n }\inℕ\)

\(\Rightarrow n=3\)