Question

If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of

x² + y²

Answer 1

x² + y²

(x² + y²) = (x + y)² - 2xy    ----(1)

Now, x + y = `(1)/((3 - 2sqrt(2))) + (1)/((3 + 2sqrt(2))`

= `((3 + 2sqrt(2)) + (3 - 2sqrt(2)))/((3 - 2sqrt(2))(3 + 2sqrt(2))`

= `(6)/(9 - 8)`

= 6

and xy = `(1)/((3 - 2sqrt(2))) xx (1)/((3 + 2sqrt(2))`

= `(1)/(9 - 8)`

= 1

substituting the valuesin (1), we get
(x² + y²)
= (x + y)² - 2xy
= 36 - 2
= 34
(x² + y²)
= 34