Question

x-1/x=root 5find x cube -1/x cube

Answer 1

$x - \frac{1}{x} = \sqrt{5 } \\ {x}^{2} + \frac{1}{ {x}^{2} } = { (x - \frac{1}{x}) }^{2} + 2 \times x \times \frac{1}{ x } \\ = {( \sqrt{5}) }^{2} + 2 = 5 + 2 = 7 \\ {x}^{3} - \frac{1}{ {x}^{3} } = (x - \frac{1}{x} )( {x}^{2} + \frac{1}{ {x}^{2} } + x \times \frac{1}{x} ) \\ = \sqrt{5} (7 + 1) = \sqrt{5 } \times 8 = 8 \sqrt{5}$