ریشهٔ سوم حاصل عبارت $\frac{۹+{{x}^{۲}}-\sqrt{{{x}^{۴}}+۲{{x}^{۲}}+۱}}{-۲\sqrt{۲}}$ کدام است؟
$\frac{9+{{x}^{2}}-\sqrt{{{({{x}^{2}}+1)}^{2}}}}{-2\sqrt{2}}=\frac{9+{{x}^{2}}-\overbrace{\left| {{x}^{2}}+1 \right|}^{+}}{-2\sqrt{2}}=\frac{9+{{x}^{2}}-{{x}^{2}}-1}{-2\sqrt{2}}=\frac{8}{-2\sqrt{2}}=\frac{{{2}^{3}}}{{{(-\sqrt{2})}^{3}}}={{(\frac{-2}{\sqrt{2}})}^{3}}\xrightarrow{rishey\,sevom}\frac{-2}{\sqrt{2}}=-\sqrt{2}$