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MathGroup Archive 2006

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Re: Solving an equation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67500] Re: Solving an equation
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 28 Jun 2006 03:52:38 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <e7qmrt$6oa$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

masha wrote:
> Hi,
> 
> I need to solve an equation (below), however, when I use Solve, I get
> an answer which I know cannot be correct (probably because Mathematica
> uses Inverse). Is their a way to get around this problem and get a true
> answer?
> 
> \!\(Assuming[\ A > 0\  && \ \
>     B\  > A\  && \ b > 1\  && \(P\^b\ Q\)\/a\  < \ \ B\  && \ \(P\^b\
> Q\)\/a \
>> A\  && \ P\^b\ Q = a\ B && \ a\  > \ 0\  && \ Co\  > \ 0\  && \ Cu\  >
>       0\  && tr\  > 0\  && \ tm > 0\  && \ Q > 0 && \ P >
>       0\  && T > 0, Solve[\(P\^\(\(-1\) - b\)\ \((\(-2\)\ a\ B\ P\^\(1
> + b\)\
>       Q + P\^\(2\ b\)\ \((P + b\ \((Co + Cu + P)\))\)\ Q\^2 - a\^2\ \((
>       A\^2\ b\ \((Co + T)\) + 2\ A\ \((\((\(-1\) + b)\)\ P - b\ Q\
>       T)\) + B\ \((\(-\((\(-2\) + B)\)\)\ P + b\ \((\(-2\)\ P +
>     B\ \((Cu +
>       P - T)\) + 2\ Q\ T)\))\))\))\)\)\/\(2\ a\ \((A - B)\)\) == 0,
> P]]\)
> 
> Thank you,
> Masha
> 
Hi Masha,

Your system seems to be inconsistent since (P^b*Q)/a < B && P^b*Q == a*B 
==> B < B.

You should eliminate the inequalities tr > 0 && tm > 0 since the 
variables tr and tm are not used in the equation.

It is best to use a replacement rule {for instance /.P^b*Q -> a*B) or a 
With clause [1] (for instance With[{B = P^b*Q/a}, ... ]) in place of the 
equality P^b*Q == a*B.

Finally, try using the built-in function Reduce [2] rather than Solve.

HTH,
Jean-Marc

[1] http://documents.wolfram.com/mathematica/functions/With

[2] http://documents.wolfram.com/mathematica/functions/Reduce


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