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))`

Rationalize the denominator:

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

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

= `(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)`

= 4