Question

va rog ajutatima cu aceste exerciti grele pentru mine.

Answer 1

$M=\left \{ x\:\in\:\mathbb{N^{*}} \:|\:\frac{20}{3x-2}\:\in\:\mathbb{N}\right \}$

$\frac{20}{3x - 2} \: \in \: \mathbb{N} = > 3x - 2 \: \in \: D_{20}$

$D_{20}=\left \{ \pm1,\pm2,\pm4,\pm5,\pm10,\pm20 \right \}$

$1)3x - 2 = - 1$

$3x = - 1 + 2$

$3x = 1$

$x = \frac{1}{3} \: \notin \: \mathbb{N^{*}}$

$2)3x - 2 = 1$

$3x = 1 + 2$

$3x = 3$

$x = \frac{3}{3}$

$x = 1 \: \in \: \mathbb{N^{*}}$

$3)3x - 2 = - 2$

$3x = - 2 + 2$

$3x = 0$

$x = \frac{0}{3}$

$x = 0 \: \notin \: \mathbb{N^{*}}$

$4)3x - 2 = 2$

$3x = 2 + 2$

$3x = 4$

$x = \frac{4}{3} \: \notin \: \mathbb{N^{*}}$

$5)3x - 2 = - 4$

$3x = - 4 + 2$

$3x = - 2$

$x = - \frac{2}{3} \: \notin \: \mathbb{N^{*}}$

$6)3x - 2 = 4$

$3x = 4 + 2$

$3x = 6$

$x = \frac{6}{3}$

$x = 2 \: \in \: \mathbb{N^{*}}$

$7)3x - 2 = - 5$

$3x = - 5 + 2$

$3x = - 3$

$x = - \frac{3}{3}$

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

$8)3x - 2 = 5$

$3x = 5 + 2$

$3x = 7$

$x = \frac{7}{3} \: \notin \: \mathbb{N^{*}}$

$9)3x - 2 = - 10$

$3x = - 10 + 2$

$3x = - 8$

$x = - \frac{8}{3} \: \notin \: \mathbb{N^{*}}$

$10)3x - 2 = 10$

$3x = 10 + 2$

$3x = 12$

$x = \frac{12}{3}$

$x = 4 \: \in \: \mathbb{N^{*}}$

$11)3x - 2 = - 20$

$3x = - 20 + 2$

$3x = - 18$

$x = - \frac{18}{3}$

$x = - 6 \: \notin \: \mathbb{N^{*}}$

$12)3x - 2 = 20$

$3x = 20 + 2$

$3x = 22$

$x = \frac{22}{3} \: \notin \: \mathbb{N^{*}}$

$x \: \in \: \mathbb{N^{*}} = > x \: \in \: \left \{ 1,2,4 \right \}$