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(1+x)(1+y)(1+z)<=4(1+xyz) with a condition on reals x,y,z

Source: RMO (Mumbai Region) 2015 P7

December 6, 2015
inequalitiesinequalities proposedtrig identitiestrigonometric substitution

Problem Statement

Let x,y,zx,y,z be real numbers such that x2+y2+z2−2xyz=1x^2+y^2+z^2-2xyz=1. Prove that (1+x)(1+y)(1+z)≤4+4xyz. (1+x)(1+y)(1+z)\le 4+4xyz.
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