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January 2nd, 2013, 12:32 AM   #1
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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(a-c)(a+b+c) = 0 How a is different from c => a-c is different from 0
How do I show that a^3 - c^3 = 0?
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January 2nd, 2013, 04:07 AM   #2
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Re: Different complex numbers equality

No one?
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January 2nd, 2013, 08:52 AM   #3
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Re: Different complex numbers equality

this one looks very easy to me :/

so

=> (1)
=> (2)
(1)+(2) ==>


so
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January 2nd, 2013, 10:35 AM   #4
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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.
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January 2nd, 2013, 11:01 AM   #5
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Re: Different complex numbers equality

Quote:
Originally Posted by gelatine1


a,b and c are different complex numbers .
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January 3rd, 2013, 12:27 AM   #6
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Re: Different complex numbers equality

Quote:
Originally Posted by zaidalyafey
Quote:
Originally Posted by gelatine1


a,b and c are different complex numbers .
o right thought these were ment to be normal variables
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