Re: Bug in Solve?
- To: mathgroup at smc.vnet.net
- Subject: [mg102954] Re: [mg102921] Bug in Solve?
- From: Tomas Garza <tgarza10 at msn.com>
- Date: Thu, 3 Sep 2009 05:38:08 -0400 (EDT)
- References: <200909020803.EAA03289@smc.vnet.net>
Oh, oh! "just can't trust Mathematica?" Sounds pretty rude in this forum.
..
Solve returns a messy expression, doesn't it? But, if you look at the solutions from a different point of view, you'll see that everything is fine:
In[1]:= sols = Solve[f[x]==0,x];
In[2]:= ComplexExpand[sols]//N
Out[2]= {{x->3.80451+0. I}, {x->-3.938+0. I}, {x->0.133492+0. I}}
It's just another way of looking at the solution. Since the coefficient of I is 0 in all three solutions, they are all real...
Tomas
> Date: Wed, 2 Sep 2009 04:03:32 -0400
> From: a2mgoog at yahoo.com
> Subject: [mg102921] Bug in Solve?
> To: mathgroup at smc.vnet.net
>
> 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.
>
- References:
- Bug in Solve?
- From: tonysin <a2mgoog@yahoo.com>
- Bug in Solve?