MathLabs

Problem 2

Let a,b,c a,b,c be positive real numbers with abc=1 abc=1. Prove that (a−1+1b)(b−1+1c)(c−1+1a)≤1(a-1+\frac1b)(b-1+\frac1c)(c-1+\frac1a)\le 1.
Step 1 of 4: Parametrize abc=1
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a=x/y,b=y/z,c=z/x.a=x/y,\quad b=y/z,\quad c=z/x.
Detailed analysis

Positive x,y,z give every positive triple with product one.