Question

If X=
$9 + 4 \sqrt{5}$
find value of
x^2 + 1/x^2

​

Answer 1

Step-by-step explanation:

$x = 9 + 4 \sqrt{5} \: \: and \: \: \frac{1}{x} = 9 - 4 \sqrt{5} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = {(x + \frac{1}{x}) }^{2} - 2 \\ \\ = {(9 + 4 \sqrt{5} + 9 - 4 \sqrt{5} )}^{2} - 2 \\ \\ = {(18)}^{2} - 2 \\ \\ = 324 - 2 = 322$