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MathGroup Archive 2007

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Re: Thread function now working as expected

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74623] Re: Thread function now working as expected
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Wed, 28 Mar 2007 04:36:23 -0500 (EST)
  • References: <euan64$do9$1@smc.vnet.net>

Copy paste the following as a whole cell in a notebook select the cell
and execute it.

In[670]:=
Print["your equality"]
eqn = Sqrt[1 + 196*x^4] == 12*x - 1 - 14*x^2
Print["square both sides"]
(#1^2 & ) /@ %%
Print["Expand both sides"]
Expand /@ %%
Print["final equation"]
(Plus[#2 - #1] & ) @@ %% == 0
Print["product of factors"]
Factor /@ %%
Print["set each factor equal to zero"]
%%[[1]] /. (a_)*(b_)*(c_Plus) -> a*b == 0 && c == 0
Print["solution"]
(Solve[#1, x] & ) /@ %%
Print["verification"]
Block[{Message}, FullSimplify[eqn /. Flatten[List @@ %%, 1]]]
Print["solution of eqn by Mathematica directly"]
Reduce[eqn, x]
{ToRules[%]}

The extreneous root x=0 is due to the process of squaring.

In[690]:=
(Solve[eqn, x, VerifySolutions -> #1] & ) /@ {True, False}

Out[690]=
{{{x -> (1/168)*(43 - I*Sqrt[167])}, {x -> (1/168)*(43 +
I*Sqrt[167])}}, {{x -> 0}, {x -> (1/168)*(43 - I*Sqrt[167])},
   {x -> (1/168)*(43 + I*Sqrt[167])}}}

Regards
Dimitris

=CF/=C7 siewsk at bp.com =DD=E3=F1=E1=F8=E5:
> I cannot get the Thread function to work on In[3] and I
> am forced to do it manually in In[4]
>
> Does anyone has any idea why In[3] is not working as I expected?
>
> In[1]:= eqn1 = Sqrt[1 + 196*x^4] == 12*x - 1 - 14*x^2
> Out[1]=
>               4                     2
> Sqrt[1 + 196 x ] == -1 + 12 x - 14 x
>
>
> In[2]:= eqn2 = Thread[(#1^2 & )[eqn1], Equal]
> Out[2]=
>          4                     2 2
> 1 + 196 x  == (-1 + 12 x - 14 x )
>
>
> In[3]:= dummy = Thread[Expand[eqn2], Equal]
> Out[3]=
>          4                     2 2
> 1 + 196 x  == (-1 + 12 x - 14 x )
>
>
> In[4]:= eqn3 = Equal[ eqn2[[1]] , Expand[ eqn2[[2]] ]  ]
> Out[4]=
>          4                    2        3        4
> 1 + 196 x  == 1 - 24 x + 172 x  - 336 x  + 196 x
>
>
> In[5]:= Simplify[eqn3]
> Out[5]=
>                   2
> x (6 - 43 x + 84 x ) == 0



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