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Bug in Solve?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102921] Bug in Solve?
  • From: tonysin <a2mgoog at yahoo.com>
  • Date: Wed, 2 Sep 2009 04:03:32 -0400 (EDT)
I am just trying to learn Mathematica. What am I doing wrong here?

I have a very simple equation:

x^3 - 15 x + 2 = 0

When I plot it in Mathematica 7,

ClearAll[*]
f[x_] := x^3 - 15 x + 2
Plot[f[x], {x, -5, 5}]


it gives the expected graph of a cubic, with three real roots near -4,
0, and 4.


When I NSolve it,

NSolve[f[x] == 0, x]

it gives

{{x -> -3.938}, {x -> 0.133492}, {x -> 3.80451}}

which is exactly what you would expect from the graph.

But when I Solve it

Solve[f[x] == 0, x]

it gives this mess

{{x -> 5/(-1 + 2 I Sqrt[31])^(1/3) + (-1 + 2 I Sqrt[31])^(
    1/3)}, {x -> -((5 (1 + I Sqrt[3]))/(
     2 (-1 + 2 I Sqrt[31])^(1/3))) -
    1/2 (1 - I Sqrt[3]) (-1 + 2 I Sqrt[31])^(1/3)}, {x -> -((
     5 (1 - I Sqrt[3]))/(2 (-1 + 2 I Sqrt[31])^(1/3))) -
    1/2 (1 + I Sqrt[3]) (-1 + 2 I Sqrt[31])^(1/3)}}


I don't know how it looks in your font, but that "I" in each solution
is the imaginary i.  Solve is saying this equation has no real roots,
even though the graph clearly shows that all three roots are real.

Can someone tell me if I am doing something wrong, or am I expecting
something wrong, or if I just can't trust Mathematica?  Thanks for any
help.
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