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Re: How to instruct Math to take a certain (e.g. real)

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  • Subject: [mg105059] Re: [mg105018] How to instruct Math to take a certain (e.g. real)
  • From: Bob Hanlon <hanlonr at>
  • Date: Thu, 19 Nov 2009 05:24:49 -0500 (EST)
  • Reply-to: hanlonr at

Your equation does not have a solution

eq = (-8 + y)^(1/3) + (8 + y)^(1/3) == y^(1/3);

Reduce[eq, y]


Solve[eq, y]


Apparently, you are looking for the solution of a different equation

f[x_] := Sign[x]*Abs[x]^(1/3)

eq2 = f[-8 + y] + f[8 + y] == f[y];

sol = {Reduce[eq2, y, Reals] // ToRadicals // ToRules}

{{y -> 0}, {y -> -12*Sqrt[3/7]}, {y -> 12*Sqrt[3/7]}}

eq2 /. sol // FullSimplify


eq /. sol


There is a legacy RealOnly add-on package at
http : //

Bob Hanlon

---- Alexei Boulbitch <Alexei.Boulbitch at> wrote: 

Dear Community,

I came to a problem, that I cannot check the solution y=0 of equation

In[345]:= eq = (-8 + y)^(1/3) + (8 + y)^(1/3) == y^(1/3);
eq /. y -> 0

Out[346]= False

just because the expression

In[347]:= eq[[1]] /. y -> 0

Out[347]= 2 + 2 (-1)^(1/3)

Mathematica does not interpret as zero. And if I ask it to give a 
numerical answer
In[348]:= 2 + 2 (-1.)^(1/3)

Out[348]= 3.+ 1.73205 \[ImaginaryI]
It returns the complex root out of the three possible.

My question is the following:

1) How should I instruct Mathematica to take a certain  root that I want 
of say, (-1)^(1/3)? 

2) I think there is a general possibility instruct Mathematica that all 
calculations should be done on reals only. Is it right?

Thank you, Alexei

Alexei Boulbitch, Dr., habil.
Senior Scientist

ZAE Weiergewan
11, rue Edmond Reuter
L-5326 Contern

Phone: +352 2454 2566
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