Junior Balkan MO 2012


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29. ožujka 2014.
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Let a,b,c be positive real numbers such that a+b+c=1. 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} \cdot \left( \sqrt{\frac{1-a}{a}}+\sqrt{\frac{1-b}{b}}+\sqrt{\frac{1-c}{c}} \right)
When does equality hold?