Question

If a, b, c are in A.P., then
$\frac{bc}{ca+ab},\frac{ca}{bc+ab},\frac{ab}{bc+ca}$ are in H.P.

• A. True
• B. False

Answer 1

The correct option is A True

We have,

$a,b,c$ are in $A.P$

$\frac{a}{abc},\frac{b}{abc},\frac{c}{abc}$ are in $A.P$

$\frac{1}{bc},\frac{1}{ca},\frac{1}{ab}$ are in $A.P$

$\frac{ab+bc+ca}{bc},\frac{ab+bc+ca}{ca},\frac{ab+bc+ca}{ab}$ are also in $A.P$

$\frac{ab+bc+ca}{bc}-1,\frac{ab+bc+ca}{ca}-1,\frac{ab+bc+ca}{ab}-1$ are also in $A.P$

$\frac{ab+ca}{bc},\frac{ab+bc}{ca},\frac{bc+ca}{ab}$ are also in $A.P$

$\frac{bc}{ab+ca},\frac{ca}{ab+bc},\frac{ab}{bc+ca}$ are in $H.P$

Hence, this is the answer.