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MathGroup Archive 2001

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Re: Solve bug !!

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31204] Re: [mg31196] Solve bug !!
  • From: BobHanlon at aol.com
  • Date: Fri, 19 Oct 2001 03:11:53 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2001/10/17 6:18:19 AM, arzo at exp.uji.es writes:

>Where is the minus sign whe must obtain in the second case??
>
>> Solve[(E^c)^2 - A*E^c + 1 == 0, c]
>
>{{c -> Log[(1/2)*(A - Sqrt[-4 + A^2])]},
>  {c -> Log[(1/2)*(A + Sqrt[-4 + A^2])]}}
>
>> Solve[(E^(-c))^2 - A*E^(-c) + 1 == 0, c]
>
>{{c -> Log[(1/2)*(A - Sqrt[-4 + A^2])]},
>  {c -> Log[(1/2)*(A + Sqrt[-4 + A^2])]}}
>
>
>Mathematica 4.1, Windows 2000 SP2, PII400.

eqn1 = (E^c)^2-A*E^c+1==0;

eqn2 = (E^(-c))^2-A*E^(-c)+1==0;

soln1 = Solve[eqn1,c];

\!\(\*FormBox[
  RowBox[{\(Solve::"ifun"\), 
    ":", "\<\"Inverse functions are being used by \
\\!\\(TraditionalForm\\`Solve\\), so some solutions may not be found.\"\>"}], 
\
TraditionalForm]\)

Verifying the results

(eqn1 /. soln1) // Simplify

{True, True}

soln2 = Solve[eqn2,c];

\!\(\*FormBox[
  RowBox[{\(Solve::"ifun"\), \(\(:\)\(\ \)\), "\<\"Inverse functions are \
being used by \\!\\(TraditionalForm\\`Solve\\), so some solutions may not be \
found.\"\>"}], TraditionalForm]\)

Again, verifying the results

(eqn2 /. soln2) // Simplify

{True, True}

In both cases there was an explicit warning that inverse functions were being 
used 
and that some solutions might not be found. Since,

soln1 == soln2

True

then, the negatives are also a solution to both equations

soln3 = (soln1 /. (x_ -> y_) :> (x -> -y));

{eqn1, eqn2} /. soln3 // Simplify

{{True, True}, {True, True}}


Bob Hanlon
Chantilly, VA  USA


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