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Chisinau MO p35 1949-56 VIII-IX 2/(c+a)=1/(b+c)+1/(a+b) if 2b^2= a^2+ c^2

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March 15, 2021
arithmetic sequencealgebra

Problem Statement

The numbers a2,b2,c2a^2, b^2, c^2 form an arithmetic progression. Show that the numbers 1b+c,1c+a,1a+b\frac{1}{b+c},\frac{1}{c+a},\frac{1}{a+b} also form arithmetic progression.
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