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8. Sequences and Series
hard
જો ${\text{x}}$ અને ${\text{y}}$ વચ્ચેનો સમગુણોતર મધ્યક ${\text{G}}$ હોય, તો $\frac{1}{{{G^2} - {x^2}}}\, + \,\frac{1}{{{G^2} - {y^2}}}$ નું મૂલ્ય થાય?
A
$G^2$
B
$2/G^2$
C
$1/G^2$
D
$3G^2$
Solution
આપેલ મુજબ ${\text{G}}\,\, = \,\,\sqrt {{\text{xy}}} $
$\therefore \,\,\frac{1}{{{G^2}\, – \,\,{x^2}}}\,\, + \,\,\frac{1}{{{G^2}\, – \,\,{y^2}}}$
$ = \,\,\frac{1}{{xy\,\, – \,\,{x^2}}}\,\, + \,\,\frac{1}{{xy\,\, – \,\,{y^2}}}$
$ \Rightarrow \,\,\,\frac{1}{{x\,\, – \,\,y}}\,\,\,\left\{ { – \frac{1}{x}\,\, + \,\,\frac{1}{y}} \right\}$
$\,\, = \,\,\frac{1}{{xy}}\,\,\,\, = \,\,\frac{1}{{{G^2}}}$
Standard 11
Mathematics
