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Question 21

If $$x = \sqrt[3]{2} + \frac{1}{\sqrt[3]{2}}$$ then the value of $$2x^3 - 6x$$ is


Correct Answer: 5

Solution

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Writing $$t=\sqrt[3]{2}$$ so $$x=t+\frac{1}{t}$$, the identity $$x^3=t^3+\frac{1}{t^3}+3x$$ gives $$x^3-3x=t^3+\frac{1}{t^3}=2+\frac{1}{2}=\frac{5}{2}$$. So $$2x^3-6x=2\left(\frac{5}{2}\right)=5$$.

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