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Real root of equation

Source: Czech and Slovak Olympiad 1955, National Round, Problem 4

August 14, 2022
quadratic polynomialequation

Problem Statement

Given that a,b,ca,b,c are distinct real numbers, show that the equation 1x−a+1x−b+1x−c=0\frac{1}{x-a}+\frac{1}{x-b}+\frac{1}{x-c}=0 has a real root.
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