OME 2007 Problem 1

Let $a_0, a_1, a_2, a_3, a_4$ be five positive numbers in the arithmetic progression with a difference $d$ . Prove that $a^3_2 \leq \frac{1}{10}(a^3_0 + 4a^3_1 + 4a^3_3 + a^3_4).$