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Inequality for real a: a + a^3 - a^4 - a^6 < 1

Source: Austrian Regional Competition for Advanced Students 2012, #1

May 23, 2012
inequalitiesinequalities proposed

Problem Statement

Prove that the inequality a+a3−a4−a6<1 a + a^3 - a^4 - a^6 < 1 holds for all real numbers aa.
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