8 Likes
– you have earned Featured Contributor Badge 
Your exceptional post has been selected for our editorial column Staff Picks http://wolfr.am/StaffPicks and Your Profile is now distinguished by a Featured Contributor Badge and is displayed on the Featured Contributor Board. Thank you!
“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.
2 Likes
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