Blazing goIITian
x=9-4root5
=> 1/x = 9+4root5
[rootx + 1/rootx]2 => x + 1/x + 2 =>9-4root5+9+4root5+2 =>20
So, rootx + 1/rootx = root20 = 2root5.
the ans. is not in the choices.
Rate, if useful. Please correct , if I am wrong.