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1 + a^{2017} + b^{2017} \geq a^{10}b^{7} + a^{7}b^{2000} + a^{2000}b^{10}

Source: Irish MO 2017 paper 2 problem 4

December 12, 2022
algebrainequalities

Problem Statement

Show that for all non-negative numbers a,ba,b, 1+a2017+b2017a10b7+a7b2000+a2000b10 1 + a^{2017} + b^{2017} \geq a^{10}b^{7} + a^{7}b^{2000} + a^{2000}b^{10} When is equality attained?