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June 5th, 2017, 01:48 AM   #1
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Empty set

If $\displaystyle f : R \rightarrow R$ is a cubic polynomial then $\{x \in R : f(x^3) = \sqrt2\}$ is an empty set ?

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June 5th, 2017, 07:00 AM   #2
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$\displaystyle (f(x^3)-\sqrt{2})$ is a polynomial of degree 9. It has a root in $\displaystyle \mathbb{R}.$
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