Question

if x = 9+4 root 3 and xy = 1 , then 1/x square + 1 /y square = ?

Answer 1

please refer to THE following attachment for the correct answer.

Answer 2

x = 9+4√3 ∴ y = 1/x =9-4√3

∴ x + y = 1 ... 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 ........................................... Ans.