1989 USAMO Problems/Problem 5

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.

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1989 USAMO (Problems • Resources)
Preceded by Problem 4	Followed by Final Question
1 • 2 • 3 • 4 • 5
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