Question

Tìm n thuộc N sao cho

n + 6 chia hết n + 2

2n + 3 chia hết n - 2

3n + 1 chia hết 11 - 2n

n² + 4 chia hết n + 1

ghi cách làm nha

Answer 1

\(a,\frac{n+6}{n+2}=\frac{n+2+4}{n+2}=1+\frac{4}{n+2}\)

Để \(n+6⋮n+2\Rightarrow\frac{4}{n+2}\in N\Leftrightarrow n+2\in\left(1;2;4\right)\)

\(\Rightarrow n\in\left(-1;0;2\right)\)

Vì \(n\in N\Rightarrow n\in\left(0;2\right)\)

\(b,2n+3⋮n-2\)

\(\Rightarrow2n-4+7⋮n-2\)

Do \(2n-4⋮n-2\Rightarrow7⋮n-2\)

\(\Rightarrow n-2\in\left(1;7\right)\)

\(\Rightarrow n\in\left(3;9\right)\)

\(d,n^2+4⋮n+1\)

\(\Rightarrow n^2+1+4⋮n+1\)

\(\Rightarrow4⋮n+1\)

\(\Rightarrow n+1\in\left(1;2;4\right)\)

\(\Rightarrow n\in\left(0;1;3\right)\)