2012 JBMO Problems/Problem 1
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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?
