Question

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

Answer 1

Given: `x - 1/x = 2`

Step-wise calculation:

1. Square both sides:

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

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

`x^2 + 1/x^2 = 4 + 2`

`x^2 + 1/x^2 = 6`

2. Use the identity:

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

Substitute the value from above:

`(x + 1/x)^2 = 6 + 2`

`(x + 1/x)^2 = 8`

3. Take the square root:

`x + 1/x = ±sqrt(8)`

`x + 1/x = ±2sqrt(2)`

So the value of `( x + 1/x)` is `±2sqrt(2)`.