If $x^4 + \frac{1}{x^4} = 1154, x > 0 $, then what will be the value of $x + \frac{1}{x} $ ?

$\sqrt{34}$ 18 $\sqrt{32}$ 6

6

We know that, 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} = 1154, x > 0 $, then x2 + \(\frac{1}{x^2}\) = \(\sqrt {1154 + 2}\) = 34 then the value of $x + \frac{1}{x} $ = \(\sqrt {34 + 2}\) = 6