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ELMO SL 2010 A2

    Let a,b,ca,b,c be positive reals. Prove that (a−b)(a−c)2a2+(b+c)2+(b−c)(b−a)2b2+(c+a)2+(c−a)(c−b)2c2+(a+b)2≥0.\frac{(a-b)(a-c)}{2a^2 + (b+c)^2} + \frac{(b-c)(b-a)}{2b^2 + (c+a)^2} + \frac{(c-a)(c-b)}{2c^2 + (a+b)^2} \geq 0.

    Calvin Deng.

    Dataset text AoPS wiki problems. Quoted with source.

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