Question

ex 11,12,13 dauuu coroanaa​

Answer 1

Explicație pas cu pas:

11. x ∈ Z

$\sqrt{15} < |x| < 23$

I)

$\sqrt{15} < x < 23$

$\sqrt{9} < \sqrt{15} < \sqrt{16} \iff 3 < \sqrt{15} < 4$

$\implies x \in \Big\{ 4; 5; 6; ...; 21; 22\Big\}$

II)

$- 23 < x < - \sqrt{15}$

$- \sqrt{16} < - \sqrt{15} < - \sqrt{9} \iff - 4 < - \sqrt{15} < - 3$

$\implies x \in \Big\{-22; - 21;...; - 6; - 5; - 4\Big\}$

=> card(M) = 38

12.

$1 \leqslant x \leqslant 2$

$x \geqslant 1 \iff x - 1 \geqslant 0 \\ \implies |x - 1| = x - 1$

$x \leqslant 2 \iff x - 2 \leqslant 0 \\ \implies |x - 2| = 2 - x$

$|x - 1| + |x - 2| = x - 1 + 2 - x = \bf 1$

13.

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

$|x + \sqrt{2} | - |x - \sqrt{2} | = x + \sqrt{2} - ( \sqrt{2} - x) = x + \sqrt{2} - \sqrt{2} + x = \bf 2x$