Question 134

If $$(x-\frac{1}{x})=3$$, then what is the value of $$(x^{3}-\frac{1}{x^{3}})$$ ?

Solution

Given : $$(x-\frac{1}{x})=3$$ ----------(i)

Cubing both sides, we get :

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

=> $$x^3-\frac{1}{x^3}-3(x)(\frac{1}{x})(x-\frac{1}{x})=27$$

=> $$x^3-\frac{1}{x^3}-3(1)(3)=27$$

=> $$(x^{3}-\frac{1}{x^{3}})=27+9=36$$

=> Ans - (A)

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