Question

If x-1/x=5, then x^3 - 1/x^3

Answer 1

Answer:

$x - \frac{1}{x} = 5 \\ cubing \: both \: sides \\ {(x - \frac{1}{x} )}^{3} = {5}^{3} \\ = > {x}^{3} - { (\frac{1}{x}) }^{3} - 3.x. \frac{1}{x} (x - \frac{1}{x} ) = 125 \\ = > {x}^{3} - \frac{1}{ {x}^{3} } - 3 \times 5 = 125 \\ = > {x}^{3} - \frac{1}{ {x}^{3} } - 15 = 125 \\ = > {x}^{3} - \frac{1}{ {x}^{3} } = 125 + 15 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 140$

the answer is 140.

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