Question

if x =
$if \: x \: = 2 + \sqrt{5} \: then \: find \: the \: value \: of \: {x}^{2} + \frac{1}{ {x}^{2} } = 18$

Answer 1

$x = 2 + \sqrt{5} \\ {x}^{2} + \frac{1}{ {x}^{2} } = (x + \frac{1}{x} )^{2} - 2 \\ substitute \: x = 2 + \sqrt{5} \: \: and \frac{1}{x} = \frac{1}{2 + \sqrt{5} }$