If $x^4 + \frac{1}{x^4} = 3842$, then the positive value of $x + \frac{1}{x}$ will be :

8

We know that,

If x⁴ + \(\frac{1}{x^4}\) = a

then x² + \(\frac{1}{x^2}\) = \(\sqrt {a + 2}\) = b

and x + \(\frac{1}{x}\) = \(\sqrt {b + 2}\)

So,

If $x^4 + \frac{1}{x^4} = 3842$,

then x² + \(\frac{1}{x^2}\) = \(\sqrt {3842 + 2}\) = 62

and x + \(\frac{1}{x}\) = \(\sqrt {62 + 2}\) = 8