Question

Tìm n > 0 để : n² + 2n + 5 chia hết cho n + 4

Answer 1

n² + 2n + 5 \(⋮n+4\)
<=> n² + 4n - 2n - 8 + 13 \(⋮n+4\)
<=> n(n+4) - 2(n+4) + 13 \(⋮n+4\)
<=> (n - 2)(n+4) + 13 \(⋮n+4\)
<=> 13 \(⋮n+4\) => n + 4 \(\inƯ\left(13\right)=\left\{\pm1;\pm13\right\}\)
=> n = -3; -5; 9; -17
Mà n > 0 <=> n = 9
@Cuber Việt