USAMO 1989 Problem 5

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.