Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2001 USAMO Problems/Problem 3

Revision as of 01:35, 21 December 2008 by Minsoens (talk | contribs) (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...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

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

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
Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2001_USAMO_Problems/Problem_3&oldid=28677"