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İnequality for all x,y,z positive real numbers

Source: Turkey Junior Math Olympiad 2018 #4

January 8, 2019
inequalitiesalgebraalgebraic inequality

Problem Statement

For all x,y,zx,y,z positive real numbers, find the all cc positive real numbers that providing x3y+y3z+z3xx+y+z+4cxyz≥2c+2\frac{x^3y+y^3z+z^3x}{x+y+z}+\frac{4c}{xyz}\ge2c+2
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