Question

If x=(3+√8), show that (x² + 1/X2) = 34​

Answer 1

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