Question

Tìm số nguyên n để 6n + 4 chia hết cho 2n + 1

Answer 1

\(\dfrac{6n+4}{2n+1}\in Z\)

\(\Rightarrow6n+4⋮2n+1\)

\(\Rightarrow6n+4-3\left(2n+1\right)⋮2n+1\)

\(\Rightarrow6n+4-6n-3⋮2n+1\)

\(\Rightarrow1⋮2n+1\)

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

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

Answer 2

\(\dfrac{6n+4}{2n+1}=\dfrac{3\left(2n+1\right)+1}{2n+1}=3+\dfrac{1}{2n+1}\)

Để \(6n+4=2n+1\Leftrightarrow1⋮2x+1\)

\(\Leftrightarrow2n+1\inƯ\left(1\right)\)

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

\(\Rightarrow2n\in\left\{0;-2\right\}\)

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

Vậy để`6n+4⋮2n+1` thì `n∈{0;-1}`