Question

If $\frac{1}{b+c},\frac{1}{c+a},\frac{1}{a+b}$ are in $A.P$., then $\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}$ are also in $G.P$

• A. True
• B. False

Answer 1

The correct option is B False

Given:

$\frac{1}{b+c},\frac{1}{c+a},\frac{1}{a+b}\text{are in}A\cdot P$

Multiply $a+b+c$

$\frac{a+b+c}{b+c},\frac{a+b+c}{c+a},\frac{a+b+c}{a+b}$ are in $A\cdot P$

$\frac{a}{b+c}+1,\frac{b}{c+a}+1,\frac{c}{a+b}+1$ are in $A\cdot P$

Subrtact 1 from each

$\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}$ are in $A\cdot P$

option $B$ is correct.