If x4 + \(\frac{1}{x^4}\) = 14159 , the positive value of x + \(\frac{1}{x}\) is?

9 17 11 15

11

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 + \(\frac{1}{x^4}\) = 14159 x2 + \(\frac{1}{x^2}\) = \(\sqrt {14159 + 2}\) = 119 So, x + \(\frac{1}{x}\) = \(\sqrt {119 + 2}\) = 11