3
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In Mathematica,

Solve[ 12 x^3 + 12 x^2 - 1 == 0]

gives

{{x -> Root[-1 + 12 #^2 + 12 #^3& , 1, 0]}, {x -> 
 Root[-1 + 12 #^2 + 12 #^3& , 2, 0]}, {x -> 
 Root[-1 + 12 #^2 + 12 #^3& , 3, 0]}}

but

== Solve 12x^3+12x^2-1=0

gives the solutions in exact form. I don't understand why Mathematica does not give the same answer as Wolfram Alpha. Any explanation?

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1 Answer 1

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Mathematica gives the same exact results only in a different representation using Root expressions.

sol = Solve[12 x^3 + 12 x^2 - 1 == 0]

enter image description here

Verifying that these are the solutions

12 x^3 + 12 x^2 - 1 == 0 /. sol // Simplify

(* {True, True, True} *)

If you prefer to see the radical representation use ToRadicals

sol // ToRadicals // TraditionalForm

enter image description here

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  • 5
    $\begingroup$ With the setting Cubics -> True, Solve[] will return Cardano-type solutions. $\endgroup$ Dec 19, 2021 at 17:48

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