Let $ a_1,a_2,...,a_6$ be real numbers such that: $ a_1 \not = 0, a_1a_6 + a_3 + a_4 = 2a_2a_5 \ \mathrm{and}\ a_1a_3 \ge a_2^2$ Prove that $ a_4a_6\le a_5^2$. When does equality holds?
Source: JBMO Shortlist 2002
Tags: inequalities, inequalities proposed
Let $ a_1,a_2,...,a_6$ be real numbers such that: $ a_1 \not = 0, a_1a_6 + a_3 + a_4 = 2a_2a_5 \ \mathrm{and}\ a_1a_3 \ge a_2^2$ Prove that $ a_4a_6\le a_5^2$. When does equality holds?