Re: solve for a squared variable

• To: mathgroup at smc.vnet.net
• Subject: [mg60469] Re: solve for a squared variable
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Sat, 17 Sep 2005 02:31:50 -0400 (EDT)
• Organization: The Open University, Milton Keynes, U.K.
• References: <200509150916.FAA15860@smc.vnet.net> <dgduk1\$19t\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Ruth Lazkoz wrote:
> Hi everyone,
>
> Why does
>
> Solve[x^2 + y == 1, x^2]
>
> give and error message? How can I solve for x^2?
>
> Thanks,
>
> Ruth
>
Hi Ruth,

Since the error message is

_General::ivar : x^2 is not a valid variable. More..._

so we must do a change of variable as in the following example:

In[1]:=
expr = x^2 + y == 1

Out[1]=
x^2 + y == 1

In[2]:=
Solve[expr /. x^2 -> X, X]

Out[2]=
{{X -> 1 - y}}

In[3]:=
x -> Sqrt[X /. %[[1]]]

Out[3]=
x -> Sqrt[1 - y]

In[4]:=
expr /. %

Out[4]=
True

Regards,
/J.M.

```

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