Question

If x=9-4√5, find the value of x2 +<br />1/x2​

Answer 1

Answer:

x = 9 - 4√5

» x + 1/x = (9 - 4√5) + 1/(9 - 4√5)

» x + 1/x = (9 - 4√5) + (9 + 4√5)/(81 - 80)

... Rationalizing

» x + 1/x = 9 - 4√5 + 9√5

» x + 1/x = 18

On squaring both sides

» x² + 1/x² + 2 (x) (1/x) = 324

» x² + 1/x² + 2 = 324

» x² + 1/x² = 322