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Easy inequality with 6 numbers

Source: JBMO Shortlist 2002

November 12, 2008
inequalitiesinequalities proposed

Problem Statement

Let a1,a2,...,a6 a_1,a_2,...,a_6 be real numbers such that: a_1 \not \equal{} 0, a_1a_6 \plus{} a_3 \plus{} a_4 \equal{} 2a_2a_5 \ \mathrm{and}\ a_1a_3 \ge a_2^2 Prove that a4a6≤a52 a_4a_6\le a_5^2. When does equality holds?
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