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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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