Question

Tìm n thuoc N

3n+7 chia het 2 n+1

 

Answer 1

3n+7 chia hết cho 2n+1

=> 6n+14 chia hết cho 2n+1

=> 6n+3+11 chia hết cho 2n+1

=> 3(2n+1) + 11 chia hết cho 2n+1

=> 11 chia hết cho 2n+1

=> 2n+1 \(\in\) Ư(11) = {1;-1;11;-11}

Vậy n \(\in\) {0;-1;5;-6}

Answer 2

Để \(3n+7⋮2n+1\)

\(\Rightarrow\left(3n+7\right)-\left(2n+1\right)⋮2n+1\)

\(\Rightarrow2.\left(3n+7\right)-3.\left(2n+1\right)⋮2n+1\)

\(\Leftrightarrow6n+14-6n-3⋮2n+1\)

\(\Leftrightarrow11⋮2n+1\)

\(\Rightarrow2n+1\) thuộc ước của 11

\(\Rightarrow n=\left\{0;5\right\}\)

Answer 3

Bổ sung: Mà n \(\in\) N => n \(\in\) {0;5) nha