Question

Va rogggg

2) Enumerati elementele multimii

A={X|X €Z\ {-2}, 5X+3 supra X+2 €Z}
Va roggg, explicati-mi pas cu pas daca se poate... am mare nevoie ma chinui de mult timp sa inteleg, dar singura nu pot!! Va rog!!!

Answer 1

$\it \dfrac{5x+3}{x+2}\in\mathbb{Z} \Rightarrow x+2|5x+3\ \ \ \ (1)\\ \\ \\ Dar\ x+2|x+2 \Rightarrow x+2|(x+2)\cdot5 \Rightarrow x+2|5x+10\ \ \ \ (2)\\ \\ \\ (1),(2) \Rightarrow x+2|5x+10-5x-3 \Rightarrow x+2|7 \Rightarrow x+2\in D_7 \Rightarrow\\ \\ \\ \Rightarrow x+2\in \{-7,\ -1\ ,1,\ 7\}|_{-2} \Rightarrow x\in\{-9,\ -3,\ -1,\ 5\}$