If x^4 + x^-4 = 194, x > 0, then what is the value of X + 1/x + 2 ?

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