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2007 Spain Mathematical Olympiad, Problem 1

Source: Spain Mathematical Olympiad 2007

June 7, 2017
algebraarithmetic sequence

Problem Statement

Let a0,a1,a2,a3,a4a_0, a_1, a_2, a_3, a_4 be five positive numbers in the arithmetic progression with a difference dd. Prove that a23≤110(a03+4a13+4a33+a43).a^3_2 \leq \frac{1}{10}(a^3_0 + 4a^3_1 + 4a^3_3 + a^3_4).
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