If $x^4 + \frac{1}{x^4}=14159$, Then a Possible value of $ x + \frac{1}{x}$is :

11

If x⁴ + \(\frac{1}{x^4}\) = a

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

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

If $x^4 + \frac{1}{x^4}=14159$

then x² + \(\frac{1}{x^2}\) = \(\sqrt {14159 + 2}\) = 119

and x + \(\frac{1}{x}\) = \(\sqrt {119 + 2}\) = 11