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

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