Question

If `x = 3 + 2sqrt(2)`, find the value of `x + 1/x`.

Answer 1

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

Step-wise calculation:

1. To find `1/x`, rationalize the denominator:

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

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

`1/x = (3 - 2sqrt(2))/(9 - 8)`

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

2. Compute `x + 1/x`:

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

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

`x + 1/x = 6`