Question 148

If $$x + \frac{1}{x} = 7$$, then $$x^3 + \frac{1}{x^3}$$ is equal to:

Solution
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We have $$x+\frac{1}{x}=7$$
Taking cubes on both sides we get :
$$x^3+\frac{1}{x^3}+3\left(x+\frac{1}{x}\right)=343$$
we get $$x^3+\frac{1}{x^3}=343-21=322$$

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