If $x+\frac{1}{x}=2 \sqrt{5}$ where x > 1, then the value of $x^3-\frac{1}{x^3}$ is:

82 76 86 78

76

If $x+\frac{1}{x}=2 \sqrt{5}$  then the value of $x^3-\frac{1}{x^3}$ ? If $x+\frac{1}{x}=n$  then,  $x-\frac{1}{x}$ = \(\sqrt {n^2 - 4}\) $x-\frac{1}{x}$= \(\sqrt {20 - 4}\) = 4 If x - \(\frac{1}{x}\)  = n then, $x^3 - \frac{1}{x^3}$ = n3 + 3 × n then, $x^3 - \frac{1}{x^3}$ = 43 + 3 × 2 = 76