Question

If `x = sqrt(2) + 1`, find `x - 1/x`.

Answer 1

Given: `x = sqrt(2) + 1`

Step-wise calculation:

1. Calculate `1/x`: 

`1/x = 1/(sqrt(2) + 1)`

= `1/(sqrt(2) + 1) xx (sqrt(2) - 1)/(sqrt(2) - 1)`

= `(sqrt(2) - 1)/((sqrt(2))^2 - 1^2)`

= `sqrt(2) - 1`

2. Find `x - 1/x`: 

`x - 1/x = (sqrt(2) + 1) - (sqrt(2) - 1)`

= `sqrt(2) + 1 - sqrt(2) + 1`

= 2