Question

Plz answer any that u know.

Answer 1

Solution 13.)

$x = 9 - 4 \sqrt{5} \\ \\ \frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} } \\ \\ \frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} } \times \frac{9 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ \frac{1}{ x} = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ \\ \frac{1}{x} = 9 + 4 \sqrt{5}$
Now,

x^2 + 1/x^2 = ( 9 - 4 root 5) ^2 + ( 9 + 4 root 5)^2

= 81 + 80 - 72 root 5 + 81 + 80 + 72 root 5

= 162 + 160

= 322