Question

If `x^2 + 1/x^2 = 23`, find the value of `x^4 + 1/x^4`.

Answer 1

Given: `x^2 + 1/x^2 = 23`

Step-wise calculation:

1. Square the given expression for `x^2 + 1/x^2`:

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

`(x^2 + 1/x^2)^2 = 529`

2. Expand the left side:

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

3. Set this equal to 529:

`x^4 + 2 + 1/x^4 = 529`

4. Subtract 2 from both sides:

`x^4 + 1/x^4 = 529 - 2`

`x^4 + 1/x^4 = 527`