If a^2, b^2, c^2 are in ap, prove that 1/(b+c), 1/(c+a), 1/(a+b) are in ap - Maths - Sequences and Series

Question

If a^2, b^2, c^2 are in ap, prove that 1/(b+c), 1/(c+a), 1/(a+b)
are in ap

Tanveer Sofi · Accepted Answer

It is given thata2, b2, c2  are in A
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⇒b2-a2=c2-b2⇒b+ab-a=c+bc-b⇒b-ab+c=c-ba+b⇒b+c-a+cb+c=c+a-b+aa+b⇒b+c-a+ca+cb+c=c+a-b+aa+ba+c⇒1a+c-1b+c=1a+b-1a+c⇒1b+c,1c+a,1a+b  are in A
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