If $$x + \frac{1}{x} = 1$$, then find the value of $$x^3 + \frac{1}{x^3}$$.
$$x+\frac{1}{x}=1.$$
So, $$x^3+\frac{1}{x^3}=\left(x+\frac{1}{x}\right)\left(x^2-x\ .\frac{1}{x}+\frac{1}{x^2}\right)=1.\left(\left(x+\frac{1}{x}\right)^2-1-2.x\ \frac{1}{x}\right)=1^2-1-2=-2.$$
D is correct choice.
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