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4ab <= 2 (a^2+ b^2) <= 5 ab if 0< a <= 2b <= 4a

Source: Austria Beginners' Competition 2012 p3

December 26, 2021
algebrainequalities

Problem Statement

Let aa and bb be two positive real numbers with a≤2b≤4aa \le 2b \le 4a. Prove that 4ab≤2(a2+b2)≤5ab4ab \le2 (a^2+ b^2) \le 5 ab.
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