Question

Tim n thuoc z biet:

1, n-4/4 thuoc z

2,n+10/n thuoc z 

3, -10/n+1 thuoc z

4, n/n-5 thuoc z

gap ậ

Answer 1

1/ Ta có \(\dfrac{n-4}{4}=\dfrac{n}{4}-1\)

Để \(\dfrac{n-4}{4}\in Z\Rightarrow\dfrac{n}{4}\in Z\Rightarrow n\in B\left(4\right)=\left\{0;4;8;12;16;20;...\right\}\)

 

2/ Ta có \(\dfrac{n+10}{n}=1+\dfrac{10}{n}\)

Để \(\dfrac{n+10}{n}\in Z\Rightarrow\dfrac{10}{n}\in Z\Rightarrow n\inƯ\left(10\right)=\left\{\pm1;\pm2;\pm5;\pm10\right\}\)

 

3/ \(-\dfrac{10}{n+1}\in Z\Rightarrow\left(n+1\right)\inƯ\left(10\right)=\left\{\pm1;\pm2;\pm5;\pm10\right\}\)

\(\Rightarrow n\in\left\{0;-2;1;-3;4;-6;9;-11\right\}\)

 

4/ Ta có \(\dfrac{n}{n-5}=\dfrac{n-5+5}{n-5}=1+\dfrac{5}{n-5}\)

Để \(\dfrac{n}{n-5}\in Z\Rightarrow\dfrac{5}{n-5}\in Z\Rightarrow\left(n-5\right)\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

\(\Rightarrow n\in\left\{6;4;10;0\right\}\)