Question

If a,b,c are in H.P., then the value of $(\frac{1}{b}+\frac{1}{c}-\frac{1}{a})(\frac{1}{c}+\frac{1}{a}-\frac{1}{b})$, is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is C

a,b,c are in H.P., then $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P.
$\Rightarrow \frac{1}{b}-\frac{1}{a}=\frac{1}{c}-\frac{1}{b}$
Now, $(\frac{1}{b}+\frac{1}{c}-\frac{1}{a})(\frac{1}{c}+\frac{1}{a}-\frac{1}{b})$
$=(\frac{3}{b}-\frac{2}{a})\left(\frac{1}{b}\right)=\frac{3}{b^2}-\frac{2}{ab}.$