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If a,b,c are in HP then show that a/b+c,b/c+a,c/a+b in HP

If a,b,c are in HP then show that a/b+c,b/c+a,c/a+b in HP

Grade:11

1 Answers

Arun
25750 Points
7 years ago
we can use reverse process here i.e.
let us assume the part which should be proved is right now we will prove the given part.
hence
 

(b+c)/a,(a+c)/b,(a+b)/c will be in a.p.

 

so (b+c)/a+1,(a+c)/b+1,(a+b)/c+1 also in a.p

 

=(a+b+c)/a,(a+b+c)/b,(a+b+c)/c

 

so1/a,1/b,1/c will be in ap

 

so a,b,c will be in h.p               

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