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