A) \[\pm \frac{1}{\sqrt{2}}\]
B) \[\pm \sqrt{2}\]
C) \[\pm \frac{1}{2\sqrt{2}}\]
D) \[\pm 2\sqrt{2}\]
Correct Answer: C
Solution :
\[1-{{x}^{4}}=64\]and \[1-{{x}^{8}}=65,\]then\[{{1}^{2}}-{{({{x}^{4}})}^{2}}=65\] \[\Rightarrow \] \[(1+{{x}^{4}})(1-{{x}^{4}})=65\] \[\Rightarrow \] \[(1+{{x}^{4}})\times 64=65\,\,\,\,\,\,[\because 1-{{x}^{4}}=64]\] \[\Rightarrow \] \[1+{{x}^{4}}=\frac{65}{64}\] \[\Rightarrow \] \[{{x}^{4}}=\frac{65}{64}-1\Rightarrow {{x}^{2}}=\pm \frac{1}{8}\] \[\therefore \] \[x=\pm \sqrt{\frac{1}{8}}=\pm \frac{1}{2\sqrt{2}}\]
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