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USAMO
1989
Problem - 3534
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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