Question

If `x + 1/x = 5`, find the value of `x^4 + 1/x^4`.

Answer 1

Given: `x + 1/x = 5`

Step-wise calculation:

1. Square both sides to find `x^2 + 1/x^2`:

`(x + 1/x)^2 = 5^2`

`x^2 + 2 + 1/x^2 = 25`

`x^2 + 1/x^2 = 25 - 2`

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

2. Square again to find `x^4 + 1/x^4`:

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

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

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

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