Question

tim so tu nhien n sao cho n^2+2 chia het cho n+2

Answer 1

\(n^2+2⋮n+2\)

Có: \(2\left(n+2\right)⋮n+2\)

=> \(2n+4⋮n+2\)

=> \(\left(n^2+2\right)+\left(2n+4\right)⋮n+2\)

=> \(n^2+2+2n+4⋮n+2\)

=> \(n^2+2n+6⋮n+2\)

=> \(n\left(n+2\right)+6⋮n+2\)

Mà \(n\left(n+2\right)⋮n+2\)

=> \(6⋮n+2\)

=> \(n+2\inƯ\left(6\right)=\left\{-6;-3;-2;-1;1;2;3;6\right\}\)

Lập bảng: 

n+2	-6	-3	-2	-1	1	2	3	6
n	-8	-5	-4	-3	-1	0	1	4