Question 152
Let $a_{0}, a_{1}, a_{2}, a_{3}, a_{4}$ be five positive numbers in arithmetic progression of ratio $d$. Prove that $$
a_{2}^{3} \leq \frac{1}{10}\left(a_{0}^{3}+4 a_{1}^{3}+4 a_{3}^{3}+a_{4}^{3}\right)
$$
a_{2}^{3} \leq \frac{1}{10}\left(a_{0}^{3}+4 a_{1}^{3}+4 a_{3}^{3}+a_{4}^{3}\right)
$$