Question

If `x = 2 + sqrt(3)`, find `x - 1/x`.

Answer 1

Given: `x = 2 + sqrt(3)`

Step-wise calculation:

1. First, find `1/x`:

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

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

= `(2 - sqrt(3))/(4 - 3)`

= `2 - sqrt(3)`

2. Now calculate `( x - 1/x)`:

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

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

= `2sqrt(3)`