A 2018-Fold Equation

★ 7/10algebraAM-GMinequalitySymmetry

Problem

Find the number of real solutions of

(x2018+1)(1+x2+x4+⋯+x2016)=2018x2017.\left(x^{2018} + 1\right)\left(1 + x^2 + x^4 + \cdots + x^{2016}\right) = 2018x^{2017}.

Answer

Solution

Difficulty7/10
Topicsalgebra, AM-GM, inequality, Symmetry

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