Question

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

• A. True
• B. False

Answer 1

The correct option is A True

We have,

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

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

On multiplying with $(a+b+c)$, we get

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

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

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

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

Hence, this is the answer.