Question

# If $x-\frac{1}{x}=3+2\sqrt{2}$, find the value of ${x}^{3}-\frac{1}{{x}^{3}}$

Solution

## In the given problem, we have to find the value of Given Cubing on both sides of we get ${\left(x-\frac{1}{x}\right)}^{3}={\left(3+2\sqrt{2}\right)}^{3}$ We shall use identity $27+16\sqrt{2}+18\sqrt{2}×3+18\sqrt{2}×2\sqrt{2}={x}^{3}-\frac{1}{{x}^{3}}-9-6\sqrt{2}\phantom{\rule{0ex}{0ex}}27+16\sqrt{2}+54\sqrt{2}+72={x}^{3}-\frac{1}{{x}^{3}}-9-6\sqrt{2}$   Hence the value of is . MathematicsRD Sharma (2017)Standard IX

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