Question

If x-1/x = 3, find the value of x^3+1/x^3​

Answer 1

$x - \frac{1}{x} = 3 \\ ( {x - \frac{1}{x} })^{2} = 9 \\ ( {x + \frac{1}{x} })^{2} - 4 = 9 \\ ( {x + \frac{1}{x} })^{2} = 13 \\ x + \frac{1}{x} = \sqrt{13} \\ \\ {x}^{3} + \frac{1}{ {x}^{ 3} } = ( {x + \frac{1}{x} })^{3} - 3(x + \frac{1}{x} ) \\ = ( { \sqrt{13} })^{3} - 3 \sqrt{13} \\ = 13 \sqrt{13} - 3 \sqrt{13} \\ = 10 \sqrt{13}$