OME 2009 Problem 5

Let, $a,b,c$ real positive numbers with $abc = 1$ Prove:

$(\frac {a}{1 + ab})^2 + (\frac {b}{1 + bc})^2 + (\frac {c}{1 + ca})^2\geq \frac {3}{4}$

Thanks!

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.