Question

if x = √2 - 1 find x2 + 1/x2​

Answer 1

$x = \sqrt{2} - 1 \\ {x}^{2} = {( \sqrt{2} - 1) }^{2} = 2 - 2 \sqrt{2} + 1 \\ {x}^{2} = 3 + 2 \sqrt{2} \\ \frac{1}{ {x}^{2} } = \frac{1}{3 + \sqrt{2} } \\ {x}^{2} + \frac{1}{ {x}^{2} } = 3 + \sqrt{2} + \frac{1}{3 + \sqrt{2} } \times \frac{3 - \sqrt{2} }{3 - \sqrt{2} } \\ = 3 + \sqrt{2} + \frac{3 - \sqrt{2} }{9 - 2} \\ = \frac{21 + 7 \sqrt{2} + 3 - \sqrt{2} }{7} \\ = \frac{24 + 6 \sqrt{2} }{7}$