# 2012 JBMO Problems/Problem 1

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

## Section 1

Let $a,b,c$ be positive real numbers such that $a+b+c=1$. Prove that $$\frac {a}{b} + \frac {a}{c} + \frac {c}{b} + \frac {c}{a} + \frac {b}{c} + \frac {b}{a} + 6 \geq 2\sqrt{2}\left (\sqrt{\frac{1-a}{a}} + \sqrt{\frac{1-b}{b}} + \sqrt{\frac{1-c}{c}}\right ).$$ When does equality hold?