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2001 USAMO Problems/Problem 3

From AoPSWiki

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.

Solution

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See also

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