Answer:
We know that \[{{(a-b)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}\] \[\therefore \] \[{{\left( x-\frac{1}{x} \right)}^{2}}={{(x)}^{2}}-2(x)\left( \frac{1}{x} \right)+{{\left( \frac{1}{x} \right)}^{2}}\] \[{{\left( x-\frac{1}{x} \right)}^{2}}={{x}^{2}}-2+\frac{1}{{{x}^{2}}}\] \[{{(7)}^{2}}={{x}^{2}}-2+\frac{1}{{{x}^{2}}}\] \[49+2={{x}^{2}}+\frac{1}{{{x}^{2}}}\] \[{{x}^{2}}+\frac{1}{{{x}^{2}}}=51\]
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