Question

Tìm n ∈ Z 

a) (n² + 5) ⋮ (n + 1)

b) (n² + 6) ⋮ (n - 1)

giúp mình với

Answer 1

a: \(\Leftrightarrow n+1\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

hay \(n\in\left\{0;-2;1;-3;2;-4;5;-7\right\}\)

b: \(\Leftrightarrow n-1\in\left\{1;-1;7;-7\right\}\)

hay \(n\in\left\{2;0;8;-6\right\}\)

Answer 2

a, \(n^2+5=n^2+n-n-1+6=n\left(n+1\right)-\left(n+1\right)+6\)

\(\Rightarrow n+1\inƯ\left(6\right)=\left\{\pm1;\pm2;\pm3;\pm6\right\}\)

n + 1	1	-1	2	-2	3	-3	6	-6
n	0	-2	1	-3	2	-4	5	-7

 

b, tương tự