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January 2nd, 2013, 12:32 AM  #1 
Newbie Joined: Dec 2012 Posts: 13 Thanks: 0  Different complex numbers equality
We have a,b,c different complex numbers so (a+b)^3 = (b+c)^3 = (c+a)^3 Show that a^3 = b^3 = c^3 From the first equality I reached a^3  c^3 + 3b(ac)(a+b+c) = 0 How a is different from c => ac is different from 0 How do I show that a^3  c^3 = 0? 
January 2nd, 2013, 04:07 AM  #2 
Newbie Joined: Dec 2012 Posts: 13 Thanks: 0  Re: Different complex numbers equality
No one?

January 2nd, 2013, 08:52 AM  #3 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: Different complex numbers equality
this one looks very easy to me :/ so => (1) => (2) (1)+(2) ==> so 
January 2nd, 2013, 10:35 AM  #4 
Newbie Joined: Dec 2012 Posts: 13 Thanks: 0  Re: Different complex numbers equality
Sorry man, it is not that simple. This problem is from the Math Gazette  high school section. As I said, I first tried to calculate (a+b)^3 = (b+c)^3 then (b+c)^3 = (a+c)^3 then (a+b)^3 = (a+c)^3 but I'm struck as I said in my first post. 
January 2nd, 2013, 11:01 AM  #5  
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Different complex numbers equality Quote:
 
January 3rd, 2013, 12:27 AM  #6  
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: Different complex numbers equality Quote:
 

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