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Inequality in three variables with sum -1

Source: MEMO 2017 T2

August 25, 2017
algebrainequalities

Problem Statement

Determine the smallest possible real constant CC such that the inequality ∣x3+y3+z3+1∣≤C∣x5+y5+z5+1∣|x^3 + y^3 + z^3 + 1| \leq C|x^5 + y^5 + z^5 + 1| holds for all real numbers x,y,zx, y, z satisfying x+y+z=−1x + y + z = -1.
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