If $x=1-sqrt{2}$, the value of $left(x-frac{1}{x} ight)^{3}$ is

$x=1-sqrt{2}$

$herefore frac{1}{x}=frac{1}{1-sqrt{2}} imes frac{1+sqrt{2}}{1+sqrt{2}}=-1-sqrt{2}$

$hereforeleft(x-frac{1}{x} ight)^{3}=(1-sqrt{2}+1+sqrt{2})^{3}=2^{3}=8$