Question

answer the following in the pic

Answer 1

$x = 3 + \sqrt{8} \\ \frac{1}{x} = \frac{1}{3 + \sqrt{8} } \times \frac{3 - \sqrt{8} }{3 - \sqrt{8} } \\ = \frac{3 - \sqrt{8} }{9 - 8} = \frac{3 - \sqrt{8} }{1} = 3 - \sqrt{8} \\ \\ x + \frac{1}{x} = 3 + \sqrt{8} + 3 - \sqrt{8} \\ x + \frac{1}{x} = 6 \\ {(x + \frac{1}{x} )}^{2} = {6}^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } +2 \times x \times \frac{1}{x} = 36 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 36 - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 34$