Question

If `x = (3 + sqrt(2))/(3 - sqrt(2)), y = (3 - sqrt(2))/(3 + sqrt(2))`, find xy.

Answer 1

Given: `x = (3 + sqrt(2))/(3 - sqrt(2)), y = (3 - sqrt(2))/(3 + sqrt(2))`

Stepwise calculation:

1. Multiply x and y: 

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

2. Since the numerator of x is the denominator of y and vice versa, the terms cancel out: 

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

xy = 1