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Algebra of Complex Numbers

If x +1/ x =8...

Question

If $x + \frac{1}{x} = 8,$ then the value of $x^{3} + \frac{1}{x^{3}}$ is

A

512

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B

488

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C

432

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D

356

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Solution

The correct option is B $488$
We know that $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
$\Rightarrow {(x + \frac{1}{x})}^{3} = x^{3} + \frac{1}{x^{3}} + 3 \times x \times \frac{1}{x} (x + \frac{1}{x})$
$\Rightarrow x^{3} + \frac{1}{x^{3}} = 8^{3} - 3 \times 8 = 488$

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