Question

if x=3-√8,find the value of x²-1/x² nd answer is -24√2​

Answer 1

$x = 3 - \sqrt{8} \\ \\ \frac{1}{x} = \frac{1}{3 - \sqrt{8} } \\ \\ \frac{1}{x} = \frac{1}{(3 - \sqrt{8} )} \frac{(3 + \sqrt{8} )}{(3 + \sqrt{8}) } \\ \\ \frac{1}{x} = 3 + \sqrt{8} \\ \\ {x}^{2} = 17 - 6 \sqrt{8} \\ \\ \frac{1}{ {x}^{2} } = 17 + 6 \sqrt{8} \\ \\ {x}^{2} - \frac{1}{ {x}^{2} } = - 12 \sqrt{8} \\ \\ {x}^{2} - \frac{1}{ {x}^{2} } = - 12 \sqrt{4 \times 2} \\ \\ {x}^{2} - \frac{1}{ {x}^{2} } = - 12 \sqrt{ {2}^{2} \times 2 } \\ \\ {x}^{2} - \frac{1}{ {x}^{2} } = - 24 \sqrt{2}$

hope it helps