rationalization

If, x = 9 + 4√5 and xy = 1 then the value of 1/x² + 1/y² = ................................

Answer:

Y = 1/x = 1/ (9 + 4√5) 

= (9 - 4√5)/{(9 + 4√5)(9 - 4√5)} 

= (9 - 4√5)/(81 – 80) 

= (9 - 4√5)

1/x² + 1/y² = (x² + y²) / x²y² 

= (81 + 80 +72√5 + 81 + 80 - 71√5)/ {(9 + 4√5)(9 - 4√5)}²

= 322 /1 = 322