Question

If `x^2 + 1/x^2 = 27`, find the value of `x - 1/x`.

Answer 1

Given: `x^2 + 1/x^2 = 27`

Step-wise calculation:

1. Recall the identity:

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

2. Using the given information, substitute `x^2 + 1/x^2 = 27` into the identity:

`(x - 1/x)^2 = 27 - 2`

 `(x - 1/x)^2 = 25`

3. Take the square root of both sides:

`x - 1/x = ±5`

So, the value of `x - 1/x` is either 5 or –5.