If x⁸ - 1442x⁴ + 1 = 0, then a possible value of $$x - \frac{1}{x}$$  is:

$$\eqalign{ & {x^8} - 1442{x^4} + 1 = 0 \cr & \frac{{{x^8}}}{{{x^4}}} - \frac{{1442{x^4}}}{{{x^4}}} + \frac{1}{{{x^4}}} = 0 \cr & {x^4} - 1442 + \frac{1}{{{x^4}}} = 0 \cr & {x^4} + \frac{1}{{{x^4}}} = 1442 \cr & {x^4} + \frac{1}{{{x^4}}} + 2 = 1444 \cr & \left( {{x^2} + \frac{1}{{{x^2}}}} \right) = 38 \cr & {x^2} + \frac{1}{{{x^2}}} - 2 = 36 \cr & {\left( {x - \frac{1}{x}} \right)^2} = 36 \cr & x - \frac{1}{x} = 6 \cr} $$