Question

If `x = 5 - 2sqrt(6)`, find the value of `1/x`.

Answer 1

Given: `x = 5 - 2sqrt(6)`

Step-wise calculation:

1. To find `1/x`, multiply the numerator and denominator by the conjugate of (x):

`1/(5 - 2sqrt(6)) xx (5 + 2sqrt(6))/(5 + 2sqrt(6)) = (5 + 2sqrt(6))/((5)^2 - (2sqrt(6))^2`

2. Simplify the denominator:

25 – 4 × 6 = 25 – 24

25 – 4 × 6 = 1

3. Thus, `1/x = 5 + 2sqrt(6)`.