Question

if f x=9-4√5 , find the value of x²+1/x²

Answer 1

Answer:

X =9 - 4 √5

1/x=1/9-4√5/9+4√5/9+4√5

1/x=9+4√5/1

x2+1/x2=(x+1/x)2-2

=(9-4√5+9+4√5)2-2

=324-2

=322. is the answer

Answer 2

Answer:

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