Mathematica returns different results when requested by Reduce, Solve

Asked Sep 18 '13 at 06:17

Active Sep 18 '13 at 06:17

Viewed 199 times

When I request with Reduce, Mathematica returns:

In[13]:= N[Reduce[X^3-26X+1 == 0,X, Reals]]                                     
Out[13]= X == -5.11814 || X == 0.0384637 || X == 5.07968

However, when I request with Solve, it returns three complex roots

In[15]:= N[Solve[X^3-26X+1 == 0,X]]                                             
                                                            -16
Out[15]= {{X -> 5.07968 + 0. I}, {X -> 0.0384637 + 4.44089 10    I}, 
                            -16
{X -> -5.11814 - 4.44089 10    I}}

I think the different here is the Reals field. However, I'm confused about the correctness of result. Which one should I follow when I want to solve the equations.

Thanks

asked Sep 18 '13 at 06:17

Loi.Luu

1

Use Chop on the results form Solve. – Kuba Sep 18 '13 at 06:28
@Kuba: it doesn't make any difference – Loi.Luu Sep 18 '13 at 06:39
2

X /. N[Solve[X^3 - 26 X + 1 == 0, X]] // Chop -> {5.07968, 0.0384637, -5.11814} which is the same result as from Reduce. – Kuba Sep 18 '13 at 06:55
2

Also, to give you refference to the answer, please take a look at difference between Solve and Reduce – Kuba Sep 18 '13 at 06:59
So I think I'd better use reduce right? – Loi.Luu Sep 18 '13 at 07:26
1

You'd better use what fits your needs :) In this particular case you can see that the result is the same. In other it can be different as described in the link I've provided. If one was absolutelly better than another what would be the purpose of the other existance? :) – Kuba Sep 18 '13 at 07:42
@Loi.Luu If you want the same result use e.g. Solve[X^3 - 26 X + 1 == 0, X, Cubics -> False]. This answer includes explanation: How do I work with Root objects?. – Artes Sep 18 '13 at 10:23

Mathematica returns different results when requested by Reduce, Solve

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