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1+1/x+1+1/y+1+1/z\ge 64 when x+y+z=1

Source: AustriaMO1970 problem 1

June 29, 2011
inequalitiesinequalities unsolved

Problem Statement

Let x,y,zx,y,z be positive real numbers such that x+y+z=1x+y+z=1 Prove that always (1+1x)×(1+1y)×(1+1z)≥64\left( 1+\frac1x\right)\times\left(1+\frac1y\right)\times\left(1 +\frac1z\right)\ge 64 When does equality hold?
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