Question

Determină x€Z:
a)3supra x-1 €Z
b)6supra x+1€Z
c)5dupra 1-x€Z

Answer 1

$a) \frac{3}{x - 1} \: \in \: \mathbb{Z} = > x - 1 \: \in \: D_{3}$

$D_{3}=\left\{\pm1,\pm3\right\}$

$1)x - 1 = - 1 = > x = 0$

$2)x - 1 = 1 = > x = 2$

$3)x - 1 = - 3 = > x = - 2$

$4)x - 1 = 3 = > x = 4$

$b) \frac{6}{x + 1} \: \in \: \mathbb{Z} = > x + 1 \: \in \: D_{6}$

$D_{6}=\left\{\pm1,\pm2,\pm3,\pm6\right\}$

$1)x + 1 = - 1 = > x = - 2$

$2)x + 1 = 1 = > x = 0$

$3)x + 1 = - 2 = > x = - 3$

$4)x + 1 = 2 = > x = 1$

$5)x + 1 = - 3 = > x = - 4$

$6)x + 1 = 3 = > x = 2$

$7)x + 1 = - 6 = > x = - 7$

$8)x + 1 = 6 = > x = 5$

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

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

$1)1 - x = - 1$

$- x = - 1 - 1$

$- x = - 2 \: | \times ( - 1)$

$x = 2$

$2)1 - x = 1$

$- x = 1 - 1$

$- x = 0 \: | \times ( - 1)$

$x = 0$

$3)1 - x = - 5$

$- x = - 5 - 1$

$- x = - 6 \: | \times ( - 1)$

$x = 6$

$4)1 - x = 5$

$- x = 5 - 1$

$- x = 4 \: | \times ( - 1)$

$x = - 4$