Question

Tìm n: a,(n+7) chia hết cho (n+2) b,(4n+9) chia hết cho(2n+2).Bài 2:cho P=5+5^3+5^5+....+5^99 a, chứng minh P chia hết cho 6 b, Tính P

Answer 1

1)

a) Ta có:

\(n+7⋮n+2\)

\(\Rightarrow\left(n+2\right)+5⋮n+2\)

\(\Rightarrow5⋮n+2\)

\(\Rightarrow n+2\in U\left(5\right)=\left\{1;5\right\}\)

+) \(n+2=1\Rightarrow n=-1\)

+) \(n+2=5\Rightarrow n=3\)

Vậy n=-1 hoặc n=3

b) Ta có:

\(4n+9⋮2n+2\)

\(\Rightarrow\left(4n+4\right)+5⋮2n+2\)

\(\Rightarrow2\left(2n+2\right)+5⋮2n+2\)

\(\Rightarrow5⋮2n+2\)

\(\Rightarrow2n+2\in U\left(5\right)=\left\{1;5\right\}\)

+) \(2n+2=1\Rightarrow n=\dfrac{-1}{2}\)

+) \(2n+2=5\Rightarrow n=\dfrac{1}{2}\)

Vậy n=-1/2 hoặc n=1/2