A) 0
B) \[-\,\,\sqrt{2}\]
C) \[-\,\,2\]
D) \[3\sqrt{2}\]
Correct Answer: C
Solution :
\[x={{(\sqrt{2}+1)}^{\frac{1}{3}}}\]\[\Rightarrow \]\[{{x}^{-3}}=\sqrt{2}+1\] \[\Rightarrow \] \[{{x}^{3}}=\frac{1}{\sqrt{2}+1}=\frac{1(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}=\sqrt{2}-1\] \[\Rightarrow \] \[\frac{1}{{{x}^{3}}}=\sqrt{2}+1\] \[\therefore \] \[{{x}^{3}}-\frac{1}{{{x}^{3}}}=\sqrt{2}-1-\sqrt{2}-1=-2\]You need to login to perform this action.
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