Question 41

If $$x + \frac{1}{x} = 1$$, then find the value of $$x^3 + \frac{1}{x^3}$$.

Solution

$$x+\frac{1}{x}=1.$$

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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RRB JE 29th May 2019 Shift-3

If $$x + \frac{1}{x} = 1$$, then find the value of $$x^3 + \frac{1}{x^3}$$.

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