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sum x/(1+yz/x) >= M if xy + yz + zx = 1

Source: 2015 Cuba 2.9

September 20, 2024
algebrainequalities

Problem Statement

Determine the largest possible value ofM M for which it holds that: x1+yzx+y1+zxy+z1+xyz≥M,\frac{x}{1 +\dfrac{yz}{x}}+ \frac{y}{1 + \dfrac{zx}{y}}+ \frac{z}{1 + \dfrac{xy}{z}} \ge M, for all real numbers x,y,z>0x, y, z > 0 that satisfy the equation xy+yz+zx=1xy + yz + zx = 1.
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