Question

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

• A. True
• B. False

Answer 1

The correct option is A True

We have,

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

$\frac{b+c-a}{a}+2,\frac{c+a-b}{b}+2,\frac{a+b-c}{c}+2$ are also in $A.P$

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

On taking common $(a+b+c)$

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

Hence, this is the answer.