Question 54

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

Solution

$$x + \frac{1}{x} = 3,$$

Cubing both side,

$$\left(x+\frac{1}{x}\right)^3=3^3$$

$$x^3+\frac{1}{x^3}+3\times\ x\times\ \frac{1}{x}\left(x+\frac{1}{x}\right)=27$$

$$x^3+\frac{1}{x^3}+3\times\ 3=27$$

$$x^3+\frac{1}{x^3}=27-9=18$$

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