Question

If x=3-√8,find x^3-1/x^3

Answer 1

$x = 3 - \sqrt{8} \\ \frac{1}{x} = \frac{1}{3 - \sqrt{8} } \\ = \frac{3 + \sqrt{8} }{ {3}^{2} - { \sqrt{8} }^{2} } \\ = \frac{3 + \sqrt{8} }{9 - 8} \\ = 3 + \sqrt{8} \\ \\ now \\ {x}- \frac{1}{ {x} } = 3 - \sqrt{8} - (3 + \sqrt{8} ) \\ = 3 - \sqrt{8} - 3 - \sqrt{8} \\ = - \sqrt{8} - \sqrt{8} \\ = - 2 \sqrt{8}$
x^3-1/x^3=(x-1/x)^3-3(x-1/x)
=(-2√8)^3-3(-2√8)
=-64√8+6√8
=-58√8