Question

Tìm các số tự nhiên n sao cho

a)2n-32 chia hết n+3

b)5n-49 chia hết n+5

Answer 1

a) \(\Rightarrow2\left(n+3\right)-38⋮\left(n+3\right)\)

Mà \(n\in N\Rightarrow n+3\ge3\)

\(\Rightarrow\left(n+3\right)\inƯ\left(38\right)=\left\{19;38\right\}\)

\(\Rightarrow n\in\left\{16;35\right\}\)

b) \(\Rightarrow5\left(n+5\right)-74⋮\left(n+5\right)\)

Do \(n\in N\Rightarrow n+5\ge5\)

\(\Rightarrow\left(n+5\right)\inƯ\left(74\right)=\left\{37;74\right\}\)

\(\Rightarrow n\in\left\{32;69\right\}\)

Answer 2

\(a,2n-32⋮n+3\Rightarrow2\left(n+3\right)-38⋮n+3\\ \Rightarrow n+3\inƯ\left(38\right)=\left\{1;2;19;38\right\}\\ \Rightarrow n\in\left\{16;35\right\}\\ b,5n-49⋮n+5\Rightarrow5\left(n+5\right)-74⋮n+5\\ \Rightarrow n+5\inƯ\left(74\right)=\left\{1;2;37;74\right\}\\ \Rightarrow n\in\left\{32;69\right\}\)

Answer 3

4^5 X 9^4-2 x 6^9/2^10 x 3^8+6^8 x 20