olymmath

BALTIC-WAY 2012 Problem 2

    Let a,b,ca, b, c be real numbers. Prove that

    ab+bc+ca+max⁡{∣a−b∣,∣b−c∣,∣c−a∣}≤1+13(a+b+c)2.a b+b c+c a+\max \{|a-b|,|b-c|,|c-a|\} \leq 1+\frac{1}{3}(a+b+c)^{2} .

    Dataset text NuminaMath olympiads. Quoted with source.

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