Difference between revisions of "2003 USAMO Problems/Problem 5"
(New page: == Problem == Let <math>a</math>, <math>b</math>, <math>c</math> be positive real numbers. Prove that <center><math>\dfrac{(2a + b + c)^2}{2a^2 + (b + c)^2} + \dfrac{(2b + c + a)^2}{2b^2 ...) |
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== Problem == | == Problem == | ||
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Let <math>a</math>, <math>b</math>, <math>c</math> be positive real numbers. Prove that | Let <math>a</math>, <math>b</math>, <math>c</math> be positive real numbers. Prove that | ||
<center><math>\dfrac{(2a + b + c)^2}{2a^2 + (b + c)^2} + \dfrac{(2b + c + a)^2}{2b^2 + (c + a)^2} + \dfrac{(2c + a + b)^2}{2c^2 + (a + b)^2} \le 8.</math></center> | <center><math>\dfrac{(2a + b + c)^2}{2a^2 + (b + c)^2} + \dfrac{(2b + c + a)^2}{2b^2 + (c + a)^2} + \dfrac{(2c + a + b)^2}{2c^2 + (a + b)^2} \le 8.</math></center> | ||
Revision as of 10:52, 8 October 2008
Problem
Let 
, 
, 
be positive real numbers. Prove that
Solution
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