Question

tìm số tự nhiên n sao cho :

a) 10 chia hết cho (n-7)

b) 42 chia hết cho (2x+3)

c) (n+10) chia hết cho (n+1)

Answer 1

a) 10 ⋮ n-7

=> n-7 \(\inƯ\left(10\right)=\left\{1;2;5;10\right\}\)

=> \(n\in\left\{8;9;12;17\right\}\)

b) 42 ⋮ 2x+3

=> 2x+3 \(\inƯ\left(42\right)=\left\{1;2;3;6;7;14;21;42\right\}\)

=> 2x \(\in\left\{0;3;4;11;18;39\right\}\)

=> x \(\in\left\{0;2;9\right\}\)

c) n+10 ⋮ n+1

=> n+1+9 ⋮  n+1

Mà n+1 ⋮  n+1

=> 9 ⋮  n+1

=> n+1 \(\inƯ\left(9\right)=\left\{1;3;9\right\}\)

=> n \(\in\left\{0;2;8\right\}\)