Question

Page 1.5
If x = 9 + 4√5 and xy = 1, then 1/x^2 + 1/y^2 is :
a) 322.....b) 155.....c) 69......d) 45

Answer 1

. x = 9 + 4√5 ∴ y = 1/x = 9 - 4√5 

∴ x + y = 18 ... and ... xy = 1 ............... (1) 
__________________________ 

∴ (1/x²) + (1/y²) 

= ( x² + y² ) / (x²y²) 

= [ (x+y)² - 2(xy) ] / (xy)² 

= [ (18)² - 2(1) ] / (1)² ............. from (1) 

= ( 324 - 2 ) / (1) 

= 322 ...............hope it may help you
.
.
.
plz mark as brainlest.......#MB

Answer 2

The answer is given below :

Given,

x = 9 + 4√5

Also,

xy = 1

=> y = 1/x

=> y = 1/(9 + 4√5)

=> y = {1/(9 + 4√5)} × {(9 - 4√5)/(9 - 4√5)}

=> y = (9 - 4√5)/(81 - 80)

=> y = 9 - 4√5

So, 1/x = 9 - 4√5 and 1/y = 9 + 4√5, since xy = 1.

Now,

1/x² + 1/y²

= (9 - 4√5)² + (9 + 4√5)²

= 81 - 72√5 + 80 + 81 + 72√5 + 80

= 322

Thus option (a) is the right answer.

Thank you for your question.