Question

If `x = 7 + 4sqrt(3)`, find the value of `1/x`.

Answer 1

Given: `x = 7 + 4sqrt(3)`

Step-wise calculation:

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

`1/(7 + 4sqrt(3)) = 1/(7 + 4sqrt(3)) xx (7 - 4sqrt(3))/(7 - 4sqrt(3))`

`1/(7 + 4sqrt(3)) = (7 - 4sqrt(3))/((7)^2 - (4sqrt(3))^2`

2. Calculate the denominator:

`7^2 - (4sqrt(3))^2 = 49 - 16 xx 3`

`7^2 - (4sqrt(3))^2 = 49 - 48`

`7^2 - (4sqrt(3))^2 = 1`

3. So, `1/x = 7 - 4sqrt(3)`.