Question

Mulţimea soluţiilor inecuaţiei |x+√3|<√3+1 este S=
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Answer 1

Explicație pas cu pas:

$|x + \sqrt{3} | < \sqrt{3} + 1$

$- (\sqrt{3} + 1) < x + \sqrt{3} < \sqrt{3} + 1 \\ - \sqrt{3} - 1 < x + \sqrt{3} < \sqrt{3} + 1\ \Big|(- \sqrt{3} )$

$- \sqrt{3} - 1 - \sqrt{3} < x + \sqrt{3} - \sqrt{3} < \sqrt{3} + 1 - \sqrt{3}$

$- 2\sqrt{3} - 1 < x < 1$

$\implies S = \Big(- 2\sqrt{3} - 1 ; 1\Big)$