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TOT 452 1995 Spring S O1 sum 1/|x-a_i| < 40 if 0<a_i<=1

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July 9, 2024
algebrainequalities

Problem Statement

Let a,b,ca, b, c and dd be points of the segment [0,1][0,1] of the real line (this means numbers xx such that 0≤x≤10 \le x \le 1). Prove that there exists a point xx on this segment such that 1∣x−a∣+1∣x−b∣+1∣x−c∣+1∣x−d∣<40.\frac{1}{|x-a|}+\frac{1}{|x-b|}+\frac{1}{|x-c|}+\frac{1}{|x-d|}< 40.
(LD Kurliandchik)
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