If $x^8 - 2599x^4 + 1= 0,$ then the positive value of $x-\frac{1}{x}$ will be :

7

If $x^8 - 2599x^4 + 1= 0,$

then the positive value of $x-\frac{1}{x}$ = ?

$x^8 - 2599x^4 + 1= 0,$

Divide by x4 on the both sides of the equation we get,

x⁴ + \(\frac{1}{x^4}\) = 2599

then, x² + \(\frac{1}{x^2}\) = \(\sqrt {2599 + 2}\) = 51

and $x-\frac{1}{x}$= \(\sqrt {51 - 2}\)  = 7