Question

If `x^4 + 1/x^4 = 527,` find the value of `x^2 + 1/x^2`

Answer 1

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

Using the identity,

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