Question

if x=9-4root5 , find the value of x square + 1/x square

Answer 1

x=9-4 root 5
1/x=9+4root5
x+1/x=18
(x+1/x)^2=x^2+1/x^2 +2
18^2=x^2 +1/x^2 +2
324=xsquare+1/xsquare +2
so xsquare +1/xsquare =322

Answer 2

{(9 - 4root5) + 1/(9 - 4root5) }^2 = (x+1/x)^2
{(9 - 4root5) + 1/(9 - 4root5) }^2= x^2 +(1/x)^2  + 2x.1/x
 {[(9 - 4root5)^2 + 1]/(9 - 4root5)}^2 = x^2  + (1/x)^2 + 2

{[(9 - 4root5)^2 + 1]/(9 - 4root5)}^2 - 2 =x^2 + (1/x)^2///---------------answer