If $x^4 + \frac{16}{x^4}= 27217, x > 0, $ then the value of $x + \frac{2}{x}$ is :

17 11 15 13

13

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 $x^4 + \frac{16}{x^4}$ = 27217, x > 0, = x2 + \(\frac{4}{x^2}\) = \(\sqrt {27217 + 2 \times 4}\) = 165 then the value of $x + \frac{2}{x}$ = \(\sqrt {165 + 2 × 2 }\) = 13