2001 USAMO Problems/Problem 3

Problem

Let $a, b, c \geq 0$ and satisfy

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

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.

Without loosing generality, we assume $(b-1)(c-1)\ge 0$ .

2001 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
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