Question

Aflați
$xez$
pentru care:
​

Answer 1

c) 14/x-7 € Z => x-7 € mulțimii divizorilor lui 14

x-7 € {-14,-7,-2,-1,1,2,7,14} |+7

x € {-7,0,5,6,8,9,14,21}

d) -17/2x+3 € Z =>2x+3 € mulțimii divizorilor lui -17

2x+3 € {-17,-1,1,17} |-3

2x € {-20,-4,-2,14} |:2

x € {-10,-2,-1, 7}

Answer 2

c)

$\it \dfrac{14}{x-7}\in\mathbb{Z}\Rightarrow x-7|14\Rightarrow x-7\in D_{14}\Rightarrow x-7\in\{\pm1,\ \pm2,\ \pm7,\ \pm14\} \Rightarrow \\ \\ x-7\in\{-14,\ -7,\ -2,\ -1,\ 1,\ 2,\ 7,\ 14\}|_{+7} \Rightarrow x\in\{-7,0,5,6,8,9,14,21\}$