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Re: Solve Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg20835] Re: [mg20813] Solve Equation
• From: adam.smith at hillsdale.edu
• Date: Wed, 17 Nov 1999 03:40:50 -0500 (EST)
• References: <80qvh7$l10@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

I believe that there was a wrong value in the set of equations given.
If I replace the L==10-6 Cos[a+b] with 13-6 Cos[a+b]:

eqn = {L==(5 + 4Cos[a]) ,L==(13 - 12 Cos[b]), L==(13 - 6Cos[a + b])}
Out[1]=
{L==5+4 Cos[a],L==13-12 Cos[b],L==13-6 Cos[a+b]}
In[2]:=
eqn/.{L->7,b -> Pi/3, a -> 5Pi/3}
Out[2]=
{True,True,True}

Interestingly, Solve finds a different solution that still works


In[3]:=
mathsolve = Solve[eqn, {L, a, b}]
Solve::"ifun":
    "Inverse functions are being used by \!\(Solve\), so some solutions
may \
not be found."
Out[3]=
                                   1
{{L -> 19 + 6 Sqrt[3], b -> ArcCos[- (-1 - Sqrt[3])],
                                   2

               1
   a -> ArcCos[- (7 + 3 Sqrt[3])]}}
               2

In[4]:=
solution = N[mathsolve]
Out[4]=
{{L -> 29.3923, b -> 3.14159 - 0.831443 I, a -> 2.49433 I}}
In[5]:=
eqn /. solution
Out[5]=
{{True,True,True}}

Adam Smith
In article <80qvh7$l10 at smc.vnet.net>,
  BobHanlon at aol.com wrote:
>
>
> The solution which you specified does not work:
>
> eqns /. {L -> 7, b -> Pi/3, a -> 5Pi/3}
>
------ Rest of message deleted --------------


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• Follow-Ups:
  • Re: Re: Solve Equation
    • From: Daniel Lichtblau <danl@wolfram.com>