2001 USAMO Problems/Problem 3

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Problem

$a^2 + b^2 + c^2 + abc = 4.$

Show that

$ab + bc + ca - abc \leq 2.$

This problem needs a solution. If you have a solution for it, please help us out by adding it.

2001 USAMO (Problems • Resources: AoPS \| ML)
Preceded by Problem 2	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 4