Question

Mă puteți ajuta vă rog cu punctul b de la exercițiul 17

Answer 1

Răspuns

Explicație pas cu pas:

Answer 2

$\it E(n)=\dfrac{3n+5}{2n-1},\ \ n\in\mathbb{Z}^*\\ \\ \\ E(n)\in\mathbb{Z} \Rightarrow \dfrac{3n+5}{2n-1}\in\mathbb{Z} \Rightarrow 2n-1|3n+5|_{\cdot2} \Rightarrow 2n-1|6n+10\ \ \ (1)\\ \\ \\ Dar,\ 2n-1|2n-1 \Rightarrow2n-1|(2n-1)\cdot3 \Rightarrow2n-1|6n-3\ \ \ (2)\\ \\ \\ (1),(2) \Rightarrow2n-1|6n+10-6n+3 \Rightarrow2n-1|13 \Rightarrow2n-1\in\{-13,-1,1,13\}|_{+1} \Rightarrow$

$\it \Rightarrow2n\in\{-12,0,2,14\}|_{:2} \Rightarrow n\in\{-6,0,1,7\}\\ \\ Dar,\ \ n\in\mathbb{Z}^*,\ \ deci\ \ A=\{-6,\ 1,\ 7\}$