Answer:
\[x-\frac{1}{x}=9\] Use the identity \[{{\left( ab \right)}^{2}}={{a}^{2}}+{{b}^{2}}2ab\] \[{{\left( x-\frac{1}{x} \right)}^{2}}={{x}^{2}}+\frac{1}{{{x}^{2}}}-2\times (x)\times \left( \frac{1}{2} \right)\] \[{{(9)}^{2}}={{x}^{2}}+\frac{1}{{{x}^{2}}}-2\] \[81+2={{x}^{2}}+\frac{1}{{{x}^{2}}}\] \[83={{x}^{2}}+\frac{1}{{{x}^{2}}}\]
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