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1/ ab +1/ bc +1/ ca =( 1/ ab + bc + ca)

Source: Polish MO second round 1952 p4

August 28, 2024
algebra

Problem Statement

Prove that if the numbers a a , b b , c c satisfy the equation 1ab+1bc+1ca=1ab+bc+ca, \frac{1}{ab} + \frac{1}{bc} +\frac{1}{ca} = \frac{1}{ab + bc + ca}, then two of them are opposite numbers.
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