A) \[\pm 8\]
B) \[10,\,\,-6\]
C) \[6,\,\,-10\]
D) \[\pm 4\]
Correct Answer: B
Solution :
\[{{x}^{2}}+\frac{1}{{{x}^{2}}}=66\] \[\Rightarrow \] \[{{\left( x-\frac{1}{x} \right)}^{2}}+2=66\] \[\Rightarrow \] \[{{\left( x-\frac{1}{x} \right)}^{2}}=66-2=64\] \[\Rightarrow \] \[x-\frac{1}{x}=\pm 8\] \[\therefore \]Expression\[=\frac{{{x}^{2}}-1+2x}{x}\] \[\frac{{{x}^{2}}}{x}-\frac{1}{x}+2=x-\frac{1}{x}+2\] Putting the value of\[x-\frac{1}{x}\] \[=8+2\]or\[-8+2=10\,\,\text{or}\,\,-6\]
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