Question

If b+c , c+a , a+b are in HP then, a/b+c , b/c+a, c/a+b are in
a)AP b)GP c)HP d)none

Answer 1

Option (C) is correct.

Given : a, b, c ... in HP ....... (1)

To Prove : a/(b+c), b/(c+a), c/(a+b) ... in HP

⇒ To Prove : (b+c)/a, (c+a)/b, (a+b)/c ... in AP

⇒ To Prove : 1+[ (b+c)/a ], 1 +[ (c+a)/b ], 1 +[ (a+b)/c ] ... in AP

⇒ To Prove : (a+b+c)/a, (a+b+c)/b, (a+b+c)/c ... in AP

⇒ To Prove : 1/a, 1/b, 1/c ... in AP

⇒ To Prove : a, b, c ... in HP, ........ which is TRUE, ... from (1).