A) \[x+\frac{1}{x}+1\]
B) \[x+\frac{1}{x}+3\]
C) \[x+\frac{1}{x}+6\]
D) \[x+\frac{1}{x}+7\]
Correct Answer: C
Solution :
\[{{x}^{2}}+\frac{1}{{{x}^{2}}}+8\left( x+\frac{1}{x} \right)+14\] \[\begin{align} & =\,\,\,\,\,\,\,\,{{\left( x+\frac{1}{x} \right)}^{2}}-2+8\left( x+\frac{1}{x} \right)+14 \\ & =\,\,\,\,\,\,\,\,{{\left( x+\frac{1}{x} \right)}^{2}}+8\left( x+\frac{1}{x} \right)+12 \\ & =\,\,\,\,\,\,\,\,{{\left( x+\frac{1}{x} \right)}^{2}}+6\left( x+\frac{1}{x} \right)+2\left( x+\frac{1}{x} \right)+12 \\ \end{align}\] \[=\,\,\,\,\,\,\,\left( x+\frac{1}{x}+2 \right)\]
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