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Inequality holds for any integer m and positive reals a, b

Source:

September 23, 2010
inductionfunctionInequalityalgebra2-variable inequalityIMO Shortlistinequalities

Problem Statement

If aa and bb are arbitrary positive real numbers and mm an integer, prove that (1+ab)m+(1+ba)m≥2m+1.\Bigr( 1+\frac ab \Bigl)^m +\Bigr( 1+\frac ba \Bigl)^m \geq 2^{m+1}.
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