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Question

If a2, b2, c2 are in A.P. show that b+c, c+a, a+b are in H.P.

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Solution

a2+c2=2b2
if a,b,c are in H.P
1a+1c=2b
1b+c+1a+b=2a+c
(a+2b+c)(a+c)=2(b+c)(a+b)a2+2ab+ac+ac+2bc+c2 =2ab+2ac+2b2+2bca2+c2=2b2

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