Question

Tìm n E(thuộc) N để:

. n+7 chai hết cho n

. n+11 chia hết cho n+9

. 2n+13 chia hết cho n+3

Answer 1

\(n+7⋮n\)

có: \(n⋮n\)

\(\Rightarrow7⋮n\)

\(\Rightarrow n\in B\left(7\right)\)

\(\Rightarrow n\in\left\{7;14;21;28;35;42;...\right\}\)

Answer 2

\(a\).

Ta có:

\(n+7⋮n\Rightarrow7⋮n\)

(Do \(n⋮n\) )

\(\Rightarrow n\inƯ\left(7\right)\Rightarrow n\in\left\{1;7\right\}\)

(Do \(n\in N\) )

b.

Ta có:

\(n+11⋮n+9\Rightarrow\left(n+9\right)+2⋮n+9\Rightarrow2⋮n+9\Rightarrow n+9\inƯ\left(2\right)\Rightarrow n+9\in\left\{\pm1;\pm2\right\}\)

\(\Rightarrow n\in\left\{-8;-7;-10;-11\right\}\)

Do n thuộc N

=>\(n\in\left\{\varnothing\right\}\)

c.Ta có:

\(2n+13⋮n+3\Rightarrow\left(2n+6\right)+7⋮n+3\Rightarrow7⋮n+3\Rightarrow n+3\inƯ\left(7\right)\)

(Do \(2n+6⋮n+3\) )

\(\Rightarrow n+3\in\left\{\pm1;\pm7\right\}\Rightarrow n\in\left\{4;-2;-4;-10\right\}\)

Do \(n\in N\Rightarrow n=4\)