Question

If `x^4 + 1/x^4 = 194, "find"  x^2 + 1/x^2`

Answer 1

Given: `x^4 + 1/x^4 = 194`

We know that,

`(x^2 + 1/x^2)^2 = x^4 + 1/x^4 + 2`   ...[Using (a + b)² = a² + b² + 2ab]

Now, substituting the given value:

`(x^2 + 1/x^2)^2 = 194 + 2`

`(x^2 + 1/x^2)^2 = 196`

`x^2 + 1/x^2 = +-sqrt196`

∴ `x^2 + 1/x^2 = +-14`