1989 USAMO Problems/Problem 5

Revision as of 16:41, 16 October 2007 by 1=2 (talk | contribs) (New page: ==Problem== Let <math>u</math> and <math>v</math> be real numbers such that <math> (u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8. </math> Det...)
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Problem

Let $u$ and $v$ be real numbers such that

$(u + u^2 + u^3 + \cdots + u^8) + 10u^9 = (v + v^2 + v^3 + \cdots + v^{10}) + 10v^{11} = 8.$

Determine, with proof, which of the two numbers, $u$ or $v$, is larger.

Solution

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