Question

Daca n ∈ natural astfel incat n + 10 supra n + 1 ∈ N

Cat este n?!? Dau coroana si 50 de puncte!

Answer 1

Răspuns:

(n+1)/(n+1)+9/(n+1)=1+9/(n+1)     n+1=D 9 ;   n+1=1 ;   n=0 ;   n+1=3 ;   n=2 ;   n+1=9 ;   n=8

Explicație pas cu pas:

Answer 2

$\it n\in\mathbb{N,\ \ } \dfrac{n+10}{n+1}\in\mathbb{N} \Rightarrow n+1|n+10\ \ \ \ \ (1)\\ \\ \\ Dar,\ \ n+1|n+1\ \ \ \ \ \ (2)\\ \\ \\ (1),\ (2)\Rightarrow n+1|n+10-n-1\Rightarrow n+1|9\Rightarrow n+1\in\{1,\ 3,\ 9\}|_{-1}\Rightarrow \\ \\ \\ \Rightarrow n\in\{0,\ \ 2,\ \ 8\}$