Question

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

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`

2. Rearrange to isolate `x^2 + 1/x^2`: 

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

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

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