Question

If $\frac{1}{ab+ac}$, $\frac{1}{bc+ab}$, $\frac{1}{ca+bc}$ are in H.P, then $a,b,c$ are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

Answer: (C)

H.P.

Given that, $\frac{1}{ab+ac}$, $\frac{1}{bc+ab}$, $\frac{1}{ca+bc}$ are in H.P
Therefore, $ab+ac$, $bc+ab$, $ca+bc$ are in A.P
$\Rightarrow 2(bc+ab)=ab+ac+ca+bc$

$\Rightarrow bc+ab=2ac$

$\Rightarrow \frac{2}{b}=\frac{1}{a}+\frac{1}{c}$
Therefore, $a$, $b$, $c$ are in H.P