#### Simfish

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"On the other hand, if [tex] \alpha[/tex] is a root of [tex]x^3 - x + 1[/tex], then [tex]\beta = \alpha^2[/tex] is a root of [tex]x^3 - 2x^2 + x - 1[/tex]. The two fields Q(\alpha) and Q(\beta) are actually equal though if we were presented only with one of the two polynomials, it might take us some time to notice how they are related."

Okay but how _are_ those two fields actually equal?