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max of M=a^2+b^2- ab when a^3 +b^3 = a^5 +b^5 (HOMC 2016 J Q3)

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August 6, 2019
inequalitiesmaximumalgebra

Problem Statement

Given two positive numbers a,ba,b such that a3+b3=a5+b5a^3 +b^3 = a^5 +b^5, then the greatest value of M=a2+b2−abM = a^2 + b^2 - ab is
(A): 14\frac14 (B): 12\frac12 (C): 22 (D): 11 (E): None of the above.
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