Question

as soon as possible please​

Answer 1

$x = 2 + \sqrt{5} \\ \frac{1}{x} = \frac{1}{2 + \sqrt{5} } \\ = \frac{1}{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} } \\ = \frac{2 - \sqrt{5} }{4 - 5} \\ = \sqrt{5} - 2 \\ x + \frac{1}{x} = 2 \sqrt{5} \\ ( {x + \frac{1}{x} })^{2} = ( {2 \sqrt{5} })^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 20 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 18$