Question

please give answer me
I give your answers​

Answer 1

x = 9 - 4√5

1/x = 1/(9 - 4√5)

Rationalize RHS:

=> 1/x = 1/(9 - 4√5) × (9 + 4√5)/(9 + 4√5)

=> x = (9 + 4√5)/(9 - 4√5)(9 + 4√5)

=> x = (9 + 4√5)/(9² - (4√5)²)

=> x = (9 + 4√5)/(81 - 80)

=> x = 9 + 4√5

Therefore,

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

Hence,

x² + 1/x² = (9 - 4√5 + 9 + 4√5)² - 2

x² + 1/x = 18² - 2 = 324 - 2 = 322