Question

If a, b, c are in G.P. then $\frac{1}{a^2 - b^2} + \frac{1}{b^2}$ is:

• A. $\frac{1}{c^2 - b^2}$
• B. $\frac{1}{b^2 - c^2}$
• C. $\frac{1}{c^2 - a^2}$
• D. $\frac{1}{b^2 - a^2}$

Answer 1

Answer: (B)

$\frac{1}{b^2 - c^2}$

Answer 2

As given : a, b, c are in G.P. $\Rightarrow b^{2 } = ac$ The given expression : $\frac{1}{a^{2} - b^{2}} + \frac{1}{b^{2}}$ $= \frac{1}{a^{2} -ac} + \frac{1}{ac}$ [using $b^2 = ac$] $= \frac{1}{a\left(a-c\right) } + \frac{1}{ac} = \frac{c+a-c}{ac\left(a-c\right)}$ $= \frac{a}{ac\left(a-c\right)} = \frac{1}{ac -c^{2}} = \frac{1}{b^{2} -c^{2}}$ [using $ac = b^2$]