Question

If a,b,c be in H.P. prove that
$\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}$ are in H.P.

Answer 1

$\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}$ will be in H.P.
if $\frac{b+c}{a},\frac{c+a}{b},\frac{a+b}{c},$ are in A.P.
Add 1 and cancel a + b + c.
that is if, $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P.
or if a,b,c are in H.P. which given.