Question

If `x^4 + 1/x^4 = 527,` find the value of `x + 1/x`

Answer 1

Given: `x^4 + 1/x^4 = 527,`

Using the identity,

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

`(x^2 + 1/x^2)^2 = 527 + 2`

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

`x^2 + 1/x^2 = +-sqrt529`

`∴x^2 + 1/x^2 = +-23`

Let’s relate it to `x + 1/x`

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

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

∴ `(x + 1/x)^2 = 23 + 2`

∴ `x + 1/x = +-sqrt25`

∴ `x + 1/x = +-5`