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1980 USAMO Problems/Problem 5

Revision as of 10:03, 5 October 2012 by 1=2 (talk | contribs) (Created page with "== Problem == If <math>x, y, z</math> are reals such that <math>0\le x, y, z \le 1</math>, show that <math>\frac{x}{y + z + 1} + \frac{y}{z + x + 1} + \frac{z}{x + y + 1} \le 1 ...")
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Problem

If $x, y, z$ are reals such that $0\le x, y, z \le 1$, show that $\frac{x}{y + z + 1} + \frac{y}{z + x + 1} + \frac{z}{x + y + 1} \le 1 - (1 - x)(1 - y)(1 - z)$

Solution

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See Also

1980 USAMO (Problems • Resources)
Preceded by
Problem 4 		Followed by
Last Question
1 • 2 • 3 • 4 • 5
All USAMO Problems and Solutions
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