If x4 + 1/(x^4) = 37634 , the positive value of x + 1/x is?

If x⁴ + \(\frac{1}{x^4}\) = a

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

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

ATQ,

x⁴ + \(\frac{1}{x^4}\) = 37634 

x² + \(\frac{1}{x^2}\) = \(\sqrt {37634 + 2}\) = 194

So, x + \(\frac{1}{x}\) = \(\sqrt {194 + 2}\) = 14