If x4 + \(\frac{1}{x^4}\) = 37634 , the positive value of x + \(\frac{1}{x}\) is?

12 14 16 11

14

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