Question

Tìm số tự nhiên n, biết: (2n + 18) chia hết cho (2n + 5)

Answer 1

Để \(2n+18⋮2n+5\)

\(\Rightarrow2n+5+13⋮2n+5\)

Vi \(2n+5⋮2n+5\)

\(\Rightarrow13⋮2n+5\)

\(\Rightarrow2n+5\inƯ\left(13\right)\)

\(\Rightarrow2n+5\in\left\{1;13\right\}\)

\(\Rightarrow n\in\left\{-2;4\right\}\)

=> n = 4

Vậy n = 4

Answer 2

\(\left(2n+18\right)⋮\left(2n+5\right)\Leftrightarrow\frac{2n+18}{2n+5}=1+\frac{13}{2n+5}\in N\Leftrightarrow\frac{13}{2n+5}\in N\)

\(\Leftrightarrow2n+5\inƯ\left(13\right)=\left\{1;13\right\}\Leftrightarrow n\in\left\{-2;4\right\}\)

mà do \(n\in N\)nên n=4