Question

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

• A. $A.P$
• B. $H.P$
• C. $G.P$
• D. Nones of these

Answer 1

Answer: (B)

$H.P$

Given a,b,c are in H.P.
so $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P
or $\frac{a+b+c}{a},\frac{b+c+a}{b},\frac{c+a+b}{c}$ are in A.P
or $\frac{b+c}{a}+1,\frac{c+a}{b}+1,\frac{a+b}{c}+1$ are in A.P
or $\frac{b+c}{a},\frac{c+a}{b},\frac{a+b}{c}$ are in A.P
or $\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}$ are in H.P
Ans: B