Question

if x-1/x=root3, find x³-1/x³​

Answer 1

Answer:

${x}^{3} - \frac{1}{ {x}^{3} } = 6 \sqrt{3}$

Step-by-step explanation:

$x - \frac{1}{x} = \sqrt{3} \\cubing \: on \: both \: the \: sides \\ {(x - \frac{1}{x} )}^{3} = {( \sqrt{3}) }^{3} \\ {(x)}^{3} - { (\frac{1}{x}) }^{3} - 3(x)( \frac{1}{x} )(x - \frac{1}{x} ) = 3 \sqrt{3} \\ {x}^{3} - \frac{1}{ {x}^{3} } - 3( \sqrt{3} ) = 3 \sqrt{3} \\ {x}^{3} - \frac{1}{ {x}^{3} } = 3 \sqrt{3} + 3 \sqrt{3} \\ {x}^{3} - \frac{1}{ {x}^{3} } = 6 \sqrt{3}$

Answer 2

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