kms - fórum o príkladoch

12. príklad 2. letnej série 2010/2011

Zadanie:
Nech $a$ , $b$ , $c$ sú kladné reálne čísla spĺňajúce $a+b+c=abc$ . Dokážte, že

$\frac{1}{\sqrt{1+a^2}} + \frac{1}{\sqrt{1+b^2}} + \frac{1}{\sqrt{1+c^2}} \leq \frac{3}{2}$

a zistite, kedy nastáva rovnosť.

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