olymmath

KZ-MO 2004 Problem 1

    For reals 1≤a≤b≤c≤d≤e≤f1\leq a\leq b \leq c \leq d \leq e \leq f prove inequality (af+be+cd)(af+bd+ce)≤(a+b2+c3)(d+e2+f3)(af + be + cd)(af + bd + ce) \leq (a + b^2 + c^3 )(d + e^2 + f^3 ) .

    Dataset text AI-MO AoPS. Quoted with source.

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