SOLUTION: if a,b,c are in h.p then prove that bc/(b+c),ca/(c+a),ab/(a+b) are in h.p

Question 461296: if a,b,c are in h.p then prove that bc/(b+c),ca/(c+a),ab/(a+b) are in h.p
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
I'm guessing "h.p." means harmonic progression? I recommend you do not use unusual abbreviations.

If a, b, c is a harmonic progression, then we can say that a = 1/k, b = 1/(k+d) and c = 1/(k+2d). We can replace the expressions for a, b, c into the next three terms:

Similarly,

We see the third, second, and first terms (in that order) follow a harmonic progression because the reciprocals of each make an arithmetic progression with common difference d.
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