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Re: Thread function now working as expected

• To: mathgroup at smc.vnet.net
• Subject: [mg74612] Re: [mg74587] Thread function now working as expected
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 28 Mar 2007 01:43:26 -0500 (EST)
• Reply-to: hanlonr at cox.net

eqn1 = Sqrt[1+196*x^4] == 12*x-1-14*x^2;

To square both sides of an equation just use Map (/@)

eqn2 = #^2& /@ eqn1

196*x^4 + 1 == (-14*x^2 + 12*x - 1)^2

To expand both sides of an equation use ExpandAll

eqn3 = eqn2//ExpandAll

196*x^4 + 1 == 196*x^4 - 336*x^3 + 172*x^2 - 24*x + 1

eqn3//Simplify

x*(84*x^2 - 43*x + 6) == 0

However, you do not need to expand eqn2 to get this result

eqn2//Simplify

x*(84*x^2 - 43*x + 6) == 0


Bob Hanlon

---- siewsk at bp.com wrote: 
> 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
> 
>