2001 USAMO Problems/Problem 3: Difference between revisions
New page: == Problem == Let <math>a, b, c \geq 0</math> and satisfy <center><math>a^2 + b^2 + c^2 + abc = 4.</math></center> Show that <center><math>ab + bc + ca - abc \leq 2.</math></center> == So... |
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== Solution == | == Solution == | ||
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Without loosing generality, we assume <math>(b-1)(c-1)\ge 0</math>. | |||
== See also == | == See also == | ||
Revision as of 21:31, 8 February 2011
Problem
Let 
and satisfy
Show that
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Without loosing generality, we assume 
.
See also
| 2001 USAMO (Problems • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
