Question 107

If $$x-\frac{1}{x}=2$$, then the value of following is: $$x^3-\frac{1}{x^3} =?$$

Solution

Given : $$x-\frac{1}{x}=2$$

Cubing both sides, we get :

=> $$(x-\frac{1}{x})^3=(2)^3$$

=> $$x^3-\frac{1}{x^3}-3(x)(\frac{1}{x})=8$$

=> $$x^3-\frac{1}{x^3}-3=8$$

=> $$x^3-\frac{1}{x^3}=8+3=11$$

=> Ans - (C)

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