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Algebraic Identities

If x=√5+√3/...

Question

If $x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ find the value of $x^{3} + \frac{1}{x^{3}}$

A

644

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B

512

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C

488

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D

348

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Solution

The correct option is C 488
$x + \frac{1}{x} = 8$
$x^{3} + \frac{1}{x^{3}} = {(x + \frac{1}{x})}^{3} - 3 (x + \frac{1}{x})$
$= 8^{3} - 3 \times 8 = 488$

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