Question

If x= 3+√8, find the value of x^2 - 1/x^2​

Answer 1

$x = 3 + \sqrt{8} \\ \frac{1}{x} = \frac{1}{3 + \sqrt{8} } \\ \frac{1}{x} = \frac{3 - \sqrt{8} }{9 - 8} \\ \frac{1}{x} = 3 - \sqrt{8} \\ \\ x + \frac{1}{x} = 6 \\ \\ x - \frac{1}{x} = 2 \sqrt{8} \\ \\ {x}^{2} - \frac{1}{ {x}^{2} } = (x + \frac{1}{x} )(x - \frac{1}{x} ) \\ = 6 \times 2 \sqrt{8} \\ = 12 \sqrt{8}$