Question

If `x^2 + 1/x^2 = 23`, find the value of `x + 1/x`.

Answer 1

Given: `x^2 + 1/x^2 = 23`

Step-wise calculation:

1. Recall the identity:

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

2. Substitute the known value:

`(x + 1/x)^2 = 23 + 2`

`(x + 1/x)^2 = 25`

3. Take the square root:

`x + 1/x = ±5`

Thus, the value of `x + 1/x` is either 5 or –5.