Question

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

Answer 1

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

Step-wise calculation:

1. Find `1/x`:

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

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

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

= `sqrt(2) - 1`

2. Find `x + 1/x`:

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

\[ x + \frac{1}{x} = 2 \sqrt{2} \]

Thus, the value of `x + 1/x` is `2sqrt(2)`.