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2012 USAJMO Problems/Problem 3

Revision as of 18:23, 24 April 2012 by Nsato (talk | contribs) (Created page with "== Problem == Let <math>a</math>, <math>b</math>, <math>c</math> be positive real numbers. Prove that <cmath>\frac{a^3 + 3b^3}{5a + b} + \frac{b^3 + 3c^3}{5b + c} + \frac{c^3 +...")
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Problem

Let $a$, $b$, $c$ be positive real numbers. Prove that \[\frac{a^3 + 3b^3}{5a + b} + \frac{b^3 + 3c^3}{5b + c} + \frac{c^3 + 3a^3}{5c + a} \ge \frac{2}{3} (a^2 + b^2 + c^2).\]

Solution

See Also

2012 USAJMO (Problems • Resources)
Preceded by
Problem 2 		Followed by
Problem 4
1 • 2 • 3 • 4 • 5 • 6
All USAJMO Problems and Solutions
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