Question

If $G$ is the geometric mean of $x$ and $y,$ then $\frac{1}{G^2-x^2}+\frac{1}{G^2-y^2}=$

• A. $G^2$
• B. $\frac{1}{G^2}$
• C. $\frac{2}{G^2}$
• D. $3G^2$

Answer 1

The correct option is B $\frac{1}{G^2}$

Given, $G=\sqrt{xy}$
$\therefore \frac{1}{G^2-x^2}+\frac{1}{G^2-y^2}=\frac{1}{xy-x^2}+\frac{1}{xy-y^2}$
$=\frac{1}{x-y}(-\frac{1}{x}+\frac{1}{y})=\frac{1}{xy}=\frac{1}{G^2}$