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[Solved] Solutions using Radicals

Posted 5 years ago
POSTED BY: Anthony Morris
4 Replies

Thank you, most useful.

POSTED BY: Anthony Morris

Thank you very much indeed, this gave me the desired result!

POSTED BY: Anthony Morris

Solve will often return Root objects since they are more concise than radicals and also have better numeric behavior. One can influence the choice of return type with the Cubics/Quartics options.

Those Root results are not approximate, by the way. The approximate values shown are from formatting of the Root values. I am not partial to that so I often use InputForm to reformat.

POSTED BY: Daniel Lichtblau
Posted 5 years ago

Try

ToRadicals[Reduce[x^4-x-2==0,x]]

which returns

x == -1 ||
x == (1 - 2*(2/(47 + 3*Sqrt[249]))^(1/3) + ((47 + 3*Sqrt[249])/2)^(1/3))/3 ||
x == 1/3 + ((1 - I*Sqrt[3])*(2/(47 + 3*Sqrt[249]))^(1/3))/3 - ((1 + I*Sqrt[3])*((47 +  3*Sqrt[249])/2)^(1/3))/6 || 
x == 1/3 + ((1 + I*Sqrt[3])*(2/(47 + 3*Sqrt[249]))^(1/3))/3 - ((1 - I*Sqrt[3])*((47 +  3*Sqrt[249])/2)^(1/3))/6
POSTED BY: Bill Nelson
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