Question

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

Answer 1

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

Step-wise calculation:

To find `1/x`, rationalise the denominator by multiplying the numerator and denominator by the conjugate `2 - sqrt(3)`:

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

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

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

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

= 4 – 3

= 1

It follows that `1/x = 2 - sqrt(3)`.