Question

DAU COROANĂ SI MAXIMUL DE PUNCTE !!! REPEDEEEEE​

Answer 1

Explicație pas cu pas:

a)

$|x - 2| \cdot ( |x - \sqrt{2}| - 2) < 0$

$x - 2 \neq 0 \iff x \neq 2$

$|x - 2| > 0 \implies |x - \sqrt{2}| - 2 < 0$

$|x - \sqrt{2}| < 2$

$- 2 < x - \sqrt{2} < 2$

$\sqrt{2} - 2 < x < \sqrt{2} + 2$

$1 < \sqrt{2} < 2 \implies - 1 < \sqrt{2} - 2 < 0$

$1 < \sqrt{2} < 2 \implies 3 < \sqrt{2} + 2 < 4$

$x \in \mathbb{{Z}^{\ast}} \implies A = \Big\{1; 3\Big\}$

b)

$|x - 2| \cdot ( |x - \sqrt{5}| - 1) < 0$

$x - 2 \neq 0 \iff x \neq 2$

$|x - 2| > 0 \implies |x - \sqrt{5}| - 1 < 0$

$|x - \sqrt{5}| < 1$

$- 1 < x - \sqrt{5} < 1$

$\sqrt{5} - 1 < x < \sqrt{5} + 1$

$2 < \sqrt{5} < 3 \implies 1 < \sqrt{5} - 1 < 2$

$2 < \sqrt{5} < 3 \implies 3 < \sqrt{5} + 1 < 4$

$x \in \mathbb{Z} \implies B = \Big\{3\Big\}$