If $x^4 + x^{-4} = 194, x > 0$, then what is the value of $X + \frac{1}{x} + 2$ ?

8 14 6 4

6

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 + x^{-4} = 194 then x2 + \(\frac{1}{x^2}\) = \(\sqrt {194 + 2}\) = 14 and x + \(\frac{1}{x}\) = \(\sqrt {14 + 2}\) = 4 $X + \frac{1}{x} + 2$ = 4 + 2 = 6