Question

Tìm số tự nhiên n để :

a)(n+6) : (n-4)

b)(2n+12) : (n-2)

Answer 1

Vì : \(\left(n+6\right)⋮\left(n-4\right)\)

Mà : \(n-4⋮\left(n-4\right)\)

\(\Rightarrow\left(n+6\right)-\left(n-4\right)⋮n-4\)

\(\Rightarrow\left(n+6-n+4\right)⋮n-4\)

\(\Rightarrow10⋮n-4\Rightarrow n-4\inƯ\left(10\right)\)

\(Ư\left(10\right)=\left\{1;2;5;10\right\}\)

+) Nếu : n - 4 = 1 => n = 5

+) Nếu : n - 4 = 2 => n = 6

+) Nếu : n - 4 = 5 => n = 9

+) Nếu : n - 4 = 10 => n = 14

Vậy : \(n\in\left\{5;6;9;14\right\}\)

b, \(\left(2n+12\right)⋮n-2\)

Mà : \(\left(n-2\right)⋮n-2\Rightarrow2\left(n-2\right)⋮n-2\Rightarrow2n-4⋮n-2\)

\(\Rightarrow\left(2n+12\right)-\left(2n-4\right)⋮n-2\)

\(\Rightarrow\left(2n+12-2n+4\right)⋮n-2\)

\(\Rightarrow16⋮n-2\)\(\Rightarrow n-2\inƯ\left(16\right)\)

\(Ư\left(16\right)=\left\{1;2;4;8;16\right\}\)

+) Nếu : n - 2 = 1 => n = 3

+) Nếu : n - 2 = 2 => n = 4

+) Nếu : n - 2 = 4 => n = 6

+) Nếu : n - 2 = 8 => n = 10

+) Nếu : n - 2 = 16 => n = 18

Vậy : \(n\in\left\{3;4;6;10;18\right\}\)

Answer 2

a, (n+6)\(⋮\)(n-4)

(n-4)+10\(⋮\)(n-4)

Vì (n-4)\(⋮\)(n-1)

Buộc 10 \(⋮\)(n-4)=>n-4ϵƯ(10)={1;2;5;10}

Với n-4=1=>n=5

n-4=2=>n=6

n-4=5=>n=9

n-4=10=>n=14

Vậy n ϵ {5;6;9;14}

Answer 3

b, (2n+12)\(⋮\)(n-2)

(2n-4)+16\(⋮\)(n-2)

2(n-2)+16\(⋮\)(n-2)

Vì (n-2)\(⋮\)(n-2)=>2(n-2)\(⋮\)(n-2)

Buộc 16 \(⋮\)(n-2)=>n-2 ϵ Ư(16)={1;2;4;8;16}

Với n-2=1=>n=3

n-2=2=>n=4

n-2=4=>n=6

n-2=8=>n=10

n-2=16=>n=18

Vậy n ϵ { 3;4;6;10;18}