Question

If x-2/x=3, find the value of x^3-8/x^3

Answer 1

$x - \frac{2}{x} = 3 \\ therefore \\ {x}^{3} - \frac{8}{ {x}^{3} } = ( {x}^{3} - { \frac{2}{x} )}^{3} = \\ {(x - \frac{2}{x}) }^{3} + 3(x)( \frac{2}{x} )(x - \frac{2}{x} ) \\ = {3}^{3} + 3(3) \\ = 27 + 9 \\ = 36$