Question : If $\small x-\frac{1}{x}=2$, then the value of $x^{3}-\frac{1}{x^{3}}$ is:
Option 1: 15
Option 2: 2
Option 3: 14
Option 4: 11
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Correct Answer: 14
Solution :
Given: $\small x-\frac{1}{x}=2$
We know that $(a-b)^3=a^3-b^3-3ab(a-b)$
So, $(x-\frac{1}{x})^3=x^3-\frac{1}{x^3}-3(x-\frac{1}{x})$
Substituting the given values, we get
⇒ $2^3=x^3 - \frac{1}{x^3}-3(2)$
⇒ $x^3 - \frac{1}{x^3}=14$
Hence, the correct answer is 14.
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