2012 JBMO Problems/Problem 1
Revision as of 18:48, 22 December 2020 by Someonenumber011 (talk | contribs) (Created page with "== Section 1 == Let <math>a,b,c</math> be positive real numbers such that <math>a+b+c=1</math>. Prove that <cmath>\frac {a}{b} + \frac {a}{c} + \frac {c}{b} + \frac {c}{a} + \...")
Section 1
Let 
be positive real numbers such that 
. Prove that
![\[\frac {a}{b} + \frac {a}{c} + \frac {c}{b} + \frac {c}{a} + \frac {b}{c} + \frac {b}{a} + 6 \geq 2\sqrt{2}\left (\sqrt{\frac{1-a}{a}} + \sqrt{\frac{1-b}{b}} + \sqrt{\frac{1-c}{c}}\right ).\]](http://latex.artofproblemsolving.com/6/0/d/60d96354dbf897c9576bd8f15779ad2e96d9fc8e.png)
When does equality hold?
