olymmath

USAMO 2011 Problem 1

  • Day 1

Let a,b,ca, b, c be positive real numbers such that a2+b2+c2+(a+b+c)2≤4a^2+b^2+c^2+(a+b+c)^2\leq4 . Prove that ab+1(a+b)2+bc+1(b+c)2+ca+1(c+a)2≥3.\frac{ab+1}{(a+b)^2}+\frac{bc+1}{(b+c)^2}+\frac{ca+1}{(c+a)^2}\geq 3.

Dataset text AI-MO AoPS. Quoted with source.

Also USAJMO 2011 Problem 2.

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