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Chisinau MO p14 1949-56 VIII-IX given 1/a+1/b+1/c=1/(a+b+c), sum of two =0

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March 15, 2021
algebraSum

Problem Statement

Prove that if the numbers a,b,ca, b, c are related by the relation 1a+1b+1c=1a+b+c\frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}= \frac{1}{a+b+c} then the sum of some two of them is equal to zero.