If $$(x+\frac{1}{x}) = k$$​ , find the value of $$x^3+ \frac{1}{x^3} .$$​​

Correct option is B

​Given:  

$$(x+\frac{1}{x}) = k$$  

Formula Used:

$$(a+b)^3= a^3 + b^3 + 3ab(a+b)$$  

Solution:

​$$(x+\frac{1}{x}) = k$$ 

Both sides doing cube 

​$$(x+\frac{1}{x})^3 = k^3$$ 

​$$x^3 + \frac{1}{x^3} +3 \times x \times \frac{1}{x}(x + \frac{1}{x}) = k^3$$ 

$$x^3 + \frac{1}{x^3} + 3k = k^3 \\\ \\x^3 +\frac{1}{x^3} = k^3 - 3k$$  ​