Question

determinați mulțimea a = {x aparține N | 18/x+3 aparține de N}

Answer 1

$a=\left\{x \: \in \: \mathbb{N} \: | \: \frac{18}{x + 3} \: \in \: \mathbb{N} \right \}$

$\frac{18}{x + 3} \: \in \: \mathbb{N} = > x + 3 \: \in \: D_{18_{+}}$

$D_{18_{+}} = \left \{ 1, 2 , 3, 6, 9, 18 \right \}$

$1)x + 3 = 1$

$x = 1 - 3$

$x = - 2 \: \notin \: \mathbb{N}$

$2)x + 3 = 2$

$x = 2 - 3$

$x = - 1 \: \notin \: \mathbb{N}$

$3)x + 3 = 3$

$x = 3 - 3$

$x = 0 \: \in \: \mathbb{N}$

$4)x + 3 = 6$

$x = 6 - 3$

$x = 3 \: \in \: \mathbb{N}$

$5)x + 3 = 9$

$x = 9 - 3$

$x = 6 \: \in \: \mathbb{N}$

$6)x + 3 = 18$

$x = 18 - 3$

$x = 15 \: \in \: \mathbb{N}$

$= > x \: \in \: \left\{0,3,6,15\right\}$

$= > a = \left\{0,3,6,15\right\}$