2000 IMO Problems/Problem 2

Problem

Let $a, b, c$ be positive real numbers with $abc=1$ . Show that

$\left( a-1+\frac{1}{b} \right)\left( b-1+\frac{1}{c} \right)\left( c-1+\frac{1}{a} \right) le 1$

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2000 IMO (Problems) • Resources
Preceded by Problem 1	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 3
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