Re: Bug in Solve?
- To: mathgroup at smc.vnet.net
- Subject: [mg17472] Re: Bug in Solve?
- From: phbrf at t-online.de (Peter Breitfeld)
- Date: Sun, 9 May 1999 04:44:04 -0400
- Organization: das ist ein breites Feld ...
- References: <7grfct$e1b@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Ilya Zavorine <iaz at cs.umd.edu> schrieb:
> I executed the following statement:
>
> Solve[1+a*b+Sqrt[1+a^2]*Sqrt[1+b^2]== 0,a]
>
> and got as the answer
>
> {{a->b}}
>
> which is obviously wrong. Is this a Mathematica bug or
> am I doing something wrong?
>
Ilya,
I think you didn't nothing wrong, but Mathematica doesn't proof the solutions of
equations. If you would try to solve this equation by hand, you get:
1+ a b = -Sqrt[1+a^2]Sqrt[1+b^2]
(1+ab)^2 = (1+a^2)(1+b^2) (*)
a^2-2ab+b^2=0
(a-b)^2=0
so a=b
But all equations can get more solutions, if you square them. This
happened here. a=b is a solution of 1+ab-Sqrt[1+a^2]Sqrt[1+b^2]=0, which
gives the equation (*) too after squaring it.
So the rule shoud be: Always proof an equation containig roots.
Es gruesst Peter
--
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Peter Breitfeld, Saulgau, Germany PGP public key: 08548045