If (x - 1/x = 4), then what is the value of(x^6 +1/(x^6)) ?

If $K-\frac{1}{K}=n$

then, $K^2+\frac{1}{K^2}$ = n² + 2

If x + \(\frac{1}{x}\)  = n

then, $x^3 +\frac{1}{x^3}$ = n³ - 3 × n

If $(x - \frac{1}{x} = 4)$

$x^2+\frac{1}{x^2}$ = 4² + 2 = 18

Cubing on both the sides,

 $x^6 +\frac{1}{x^6}$ = 18³ - 3 × 18 = 5832 - 54

Then the value of$(x^6 +\frac{1}{x^6})$ = 5778