Question

Dau coroana, multumeesc

Answer 1

$a) \frac{5}{x - 1} \: \in\: \mathbb{Z} = > (x - 1) \: \in \: D_{5}$

$D_{5}=\left\{\pm1,\pm5\right\}$

$1)x - 1 = - 1$

$x = - 1 + 1$

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

$2)x - 1 = 1$

$x = 1 + 1$

$x = 2 \: \in \: \mathbb{Z}$

$3)x - 1 = - 5$

$x = - 5 + 1$

$x = - 4 \: \in \: \mathbb{Z}$

$4)x - 1 = 5$

$x = 5 + 1$

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

$= > x \: \in \: \left\{-4,0,2,6\right\}$

$b) |x - 5| = 1$

$1)x - 5 = 1$

$x = 1 + 5$

$x = 6$

$2)x - 5 = - 1$

$x = - 1 + 5$

$x = 4$

$S=\left\{4,6\right\}$