Question

If $x-\frac{1}{x}=3$ then find the value of $x^3-\frac{1}{x^3}$

Answer 1

$\begin{array}{c}Wehave\\ x-\frac{1}{x}=3\\ Now,\\ {\left(x-\frac{1}{x}\right)}^3=x^3-\frac{1}{x^3}-3\times x\times \frac{1}{x}\left(x-\frac{1}{x}\right)\\ {\left(3\right)}^3=x^3-\frac{1}{x^3}-3\left(3\right)\\ x^3-\frac{1}{x^3}={\left(3\right)}^3+3\times 3\\ =27+6\\ =36\\ Hence,\\ x^3-\frac{1}{x^3}=36.\end{array}$