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Roots in polynomials

Source: Moscow Math Olympiad 2017, Grade 11, P3

April 25, 2017
algebrapolynomialinequalities

Problem Statement

Let x0x_0 - is positive root of x2017x1=0x^{2017}-x-1=0 and y0y_0 - is positive root of y4034y=3x0y^{4034}-y=3x_0 a) Compare x0x_0 and y0y_0 b) Find tenth digit after decimal mark in decimal representation of x0y0|x_0-y_0|