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\frac{m^2}{a-x} + \frac{n^2}{b-x} = 1

Source: Polish MO second round 1951 p3

August 28, 2024
algebra

Problem Statement

Prove that the equation m2a−x+n2b−x=1,\frac{m^2}{a-x} + \frac{n^2}{b-x} = 1, where m≠0 m \ne 0 , n≠0 n \ne 0 , a≠b a \ne b , has real roots (m m , n n , a a , b b denote real numbers).
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