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No way to express these real numbers with real radicals!

Posted 2 months ago
3 Replies
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3 Replies

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"A cubic can have all three roots real, yet inexpressible with real radicals!"

She even has a name (casus irreducibilis). Inconvenient for Galois if he was shot over this since it was hardly his fault. But maybe the shooter was irrational...

"Cops out completely and says to do it numerically!"

No, not really. This is just the display format for Root objects. Some people apparently like it. Don't ask me why, I have no idea.

What about this?

Solve[8 x^3 == 6 x + 1, x] // FullSimplify
Solve[PolynomialQuotient[8 x^3 - 6 x - 1, x - Cos[\[Pi]/9], x] == 0,   x] // FullSimplify
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