MathDB

5

Part of 2009 Spain Mathematical Olympiad

Problems(1)

(a/(1 + ab))^2 + (b/(1 + bc))^2 + (c/(1 + ca))^2 ≥ 3/4

Source: Spain National Olympiad (OME) 2009, Problem 4

12/29/2009
Let, a,b,c a,b,c real positive numbers with abc \equal{} 1 Prove: (\frac {a}{1 \plus{} ab})^2 \plus{} (\frac {b}{1 \plus{} bc})^2 \plus{} (\frac {c}{1 \plus{} ca})^2\geq \frac {3}{4} Thanks!
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