Re: How to use "Solve" to get only real number solutions?

• To: mathgroup at smc.vnet.net
• Subject: [mg55151] Re: How to use "Solve" to get only real number solutions?
• From: Peter Pein <petsie at arcor.de>
• Date: Mon, 14 Mar 2005 03:43:56 -0500 (EST)
• References: <d114lb\$e18\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```PengYu.UT at gmail.com wrote:
> Hi All
>
> For example I have the following function and I want to find the
> solution of the quation shown below. But Mathematica showns not only
> real number solutions. Do you know how to restrict the solutions to
> only real numbers. Thanks!
>
> Best wishes,
> Peng
>
> intensity[x_, Î´_, p_, Î»_] := 1/4 + (2*Cos[(Pi*x)/100])/Pi +
> (4*Cos[(Pi*x)/100]^2)/Pi^2 - (2*Cos[(3*Pi*x)/100])/(3*Pi) -
>  (8*Cos[(Pi*x)/100]*Cos[(3*Pi*x)/100])/(3*Pi^2) +
> (4*Cos[(3*Pi*x)/100]^2)/(9*Pi^2)
>
> Solve[intensity[x, 0, 200, 50] == 0.3*(1/4 + 32/(9*Pi^2) +
> (4*Sqrt[2])/(3*Pi)), x]
>
Hi Peng,

you can either select the reals after computation of all solutions:

Select[x /. Solve[intensity[x, 0, 200, 50] ==
3/10*(1/4 + 32/(9*Pi^2) + (4*Sqrt[2])/(3*Pi)), x],
Im[Chop[N[#]]] == 0 &]

or use Reduce:

Reduce[intensity[x, 0, 200, 50] == 3/10*(1/4 + 32/(9*Pi^2) +
(4*Sqrt[2])/(3*Pi)), x, Reals]

--
Peter Pein
Berlin

```

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