If G be geometric mean of x and y , then frac{1}{{{G^2} - {x^2}}} + frac{1}{{{G^2} - {y^2}}} =

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8. Sequences and Series

easy

If $G$ be 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

$3{G^2}$

Solution

(b) As 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}}\left\{ { – \frac{1}{x} + \frac{1}{y}} \right\} = \frac{1}{{xy}} = \frac{1}{{{G^2}}}$.

Standard 11

Mathematics

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