Question

determinati multimea a={x€z|3x+5/x-1€Z,xnu este egal cu 1}​

Answer 1

Răspuns:

Explicație pas cu pas:

Poza

Answer 2

$\it \dfrac{3x+5}{x-1}\in\mathbb{Z} \Rightarrow x-1|3x+5\ \ \ \ (1)\\ \\ \\ Dar,\ x-1|x-1 \Rightarrow x-1|(x-1)\cdot3 \Rightarrow x-1|3x-3\ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow x-1|3x+5-(3x-3) \Rightarrow x-1|3x+5-3x+3 \Rightarrow x-1|8\Rightarrow \\ \\ \\ \Rightarrow x-1\in\{\pm1,\ \pm2,\ \pm4,\ \pm8\}\Rightarrow x-1\in\{-8,-4,-2,-1,1,2,4,8\}|_{+1}\Rightarrow$

$\it \Rightarrow x\in\{-7,\ -3,\ -1,\ 0,\ 2,\ 3,\ 5,\ 9\}$

Prin urmare,  A = {-7, -3, -1, 0, 2, 3, 5, 9}