Question

If x² – 6x + 1 = 0, find the value of `x^2 + 1/x^2`.

Answer 1

Given: x² – 6x + 1 = 0

Step-wise calculation:

1. Divide the entire equation by (x) assuming (x ≠ 0):

`x - 6 + 1/x = 0`

2. Rewrite it as:

`x + 1/x = 6`

3. Square both sides:

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

`x^2 + 2 + 1/x^2 = 36`

4. Subtract 2 from both sides:

`x^2 + 1/x^2 = 36 - 2`

`x^2 + 1/x^2 = 34`

Therefore, the value of `x^2 + 1/x^2` is 34.