2001 USAMO Problems/Problem 3
Problem
Let and satisfy
![$a^2 + b^2 + c^2 + abc = 4.$](http://latex.artofproblemsolving.com/1/6/e/16e70ab813b2e9287a1015d7b890d16f94a7073e.png)
Show that
![$ab + bc + ca - abc \leq 2.$](http://latex.artofproblemsolving.com/6/6/c/66c37e5bd5601bffeb016667562ca756e7dd1d9b.png)
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 |