Question

a)4n-28 chia hết cho 2n-22

b)7n-1 chia hết cho 11-n

Answer 1

Ta có :\(4n-28⋮2n-22\)

\(\Rightarrow4n-44+16⋮2n-22\)

Mà \(4n-44⋮2n-22\Rightarrow16⋮n-22\)

\(\Rightarrow n-22\inƯ\left(16\right)=\left\{1;2;4;8;16\right\}\)

+ \(n-22=1\Rightarrow n=23\)

+ \(n-22=2\Rightarrow n=24\)

+ \(n-22=4\Rightarrow n=26\)

+ \(n-22=8\Rightarrow n=30\)

+ \(n-22=16\Rightarrow n=38\)

Vậy \(n\in\left\{23;24;26;30;38\right\}\)

Answer 2

a) \(A=2+\dfrac{8}{n+11}\)

A nguyên => n-11 thuộc ước 8 =>
n-11 ={-8,-4,-2,-1,1,2,4,8)
n ={3,7,9,10,11,13,15,19}