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Re: Only real solutions for a=a^0.7*b

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  • Subject: [mg119733] Re: Only real solutions for a=a^0.7*b
  • From: Dana DeLouis <dana.del at gmail.com>
  • Date: Sun, 19 Jun 2011 19:28:42 -0400 (EDT)

Hi.  Given an example like this:

equ=3 x^3+4 x-7.0;
Solve[equ==0,x]
{
{x->-0.5-1.44338 I},
{x->-0.5+1.44338 I},
{x->1.}
}

Sometimes this works:

Solve[equ==0,x,Reals]
{{x->1.}}

However, your example returned a ConditionalExpression

eq =  a==a^0.7*b ;
Solve[eq,a,Reals]
<...>

Probably not the best way, but here's one idea:

NoComplex[v_]:=Length[Position[v,_Complex,\[Infinity],Heads->True]]==0

eq =  a==a^0.7*b ;
Solve[eq,a] //NoComplex

{{a->0.},{a->1. b^(10/3)}}

Another example:

equ = 3 x^3 + 4 x - 7.0;
Solve[equ == 0, x]

{{x -> -0.5 - 1.44338 I}, {x -> -0.5 + 1.44338 I}, {x -> 1.}}

Solve[equ == 0, x] // NoComplex

{{x -> 1.}}

= = = = = = = = = =
HTH  : >)
Dana DeLouis
$Version
8.0 for Mac OS X x86 (64-bit) (November 6, 2010)


On Jun 18, 7:54 pm, "niels.gie... at gmail.com" <niels.gie... at googlemail.com> wrote:
> Hi all!
>
> Is there a way to make Mathematica only report the real solution for
>
> eq = a == a^0.7*b
>
> Solve[eq, a]
>
> reports:
> {{a -> 0.}, {a -> (-0.5 - 0.866025 I) b^(
>     10/3)}, {a -> (-0.5 + 0.866025 I) b^(10/3)}, {a -> 1. b^(10/3)}}
>
> The solution I am after is the last one. Is there a way to have solve
> only report that one? As the exponent is changing from case to case
> selecting one like [[5]] does not help. Playing around with Refine[],
> Assuming[] etc. to impose a>0 did not help.
>
> Does someone have a hint for me how to do this? I am using Mathematica
> 7.0.0 (Windows, 64 bit)
>
> Cheers,
>
> Niels




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