If $$x + x^{-1}$$ = 7, then find the value of $$x^3 + x^{-3}$$.​

Correct option is C

Given:

​$$x + \frac{1}{x} = 7$$ 

Formula Used:

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

Solution:

​$$x^3+\frac{1}{x^3}= (7)^3 - 3\times 7\\x^3+\frac{1}{x^3}= 343 - 21 \\x^3+\frac{1}{x^3}= 322$$

hence, option (c) is the correct answer.