MathDB

4

Part of 1955 Czech and Slovak Olympiad III A

Problems(1)

Real root of equation

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

8/14/2022
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.
quadratic polynomialequation