Question

If `x - 1/x = 4`, find the value of `x^2 + 1/x^2`.

Answer 1

Given: `x - 1/x = 4`

Step-wise calculation:

1. Square both sides:

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

`x^2 - 2 + 1/x^2 = 16`

2. Rearrange the equation:

`x^2 + 1/x^2 - 2 = 16`

`x^2 + 1/x^2 = 16 + 2`

`x^2 + 1/x^2 = 18`