Question

If `x + 1/x = 5`, find the value of `x - 1/x`.

Answer 1

Given: `x + 1/x = 5`

Step-wise calculation:

1. We want to find `x - 1/x`.

2. Start with the identity:

`(x - 1/x)^2 = (x + 1/x)^2 - 4 xx x xx 1/x`

`(x - 1/x)^2 = (x + 1/x)^2 - 4`

3. Substitute `x + 1/x = 5`:

`(x - 1/x)^2 = 5^2 - 4`

`(x - 1/x)^2 = 25 - 4`

`(x - 1/x)^2 = 21`

4. So, `x - 1/x = ±sqrt(21)`

The value of `x - 1/x` is `±sqrt(21)`.