USA Mathematical Olympiad 1989 Problem
Which is larger, the real root of $x + x^2 + ... + x^8 = 8 - 10x^9$, or the real root of $x + x^2 + ... + x^{10} = 8 - 10x^{11}$?
The upper part of the solution below is mine and the lower part belongs to the math professor from Arizona, USA.