If $$x - \frac{1}{x} = 10$$, then the value of $$x^3 - \frac{1}{x^3}$$ is:​

Correct option is B

Given:

​$$x-\dfrac{1}{x}=10$$​​

Find $$x^{3}-\dfrac{1}{x^{3}}$$​​​​

Solution:

​$$(x-\frac{1}{x})^{2}=x^{2}+\frac{1}{x^{2}}-2$$​​

$$x^{2}+\frac{1}{x^{2}}=10^{2}+2=102$$​​

​$$x^{3}-\frac{1}{x^{3}}=(x-\frac{1}{x})\left(x^{2}+\frac{1}{x^{2}}+1\right)=10(102+1)=10\times 103=1030$$​​