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Topic: More algebraic proofs
Replies: 5   Last Post: Apr 28, 2005 10:50 AM

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Posts: 22
Registered: 12/6/04
More algebraic proofs
Posted: Apr 23, 2005 1:28 PM
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Hello, all!
I have to prove the following:
if a + b + c = 0, then (a^2 + b^2 + c^2)^2 = 2(a^4 + b^4 + c^4).

Here is what I have so far:

I worked out the square for the left side, and got
a^4 + b^4 + c^4 + 2(a^2b^2 + a^2c^2 + b^2c^2). Taking out the ^4
terms, I now have a new equality to prove:

2(a^2b^2 + a^2c^2 + b^2c^2) = a^4 + b^4 + c^4

I tried several approaches, without success.
I tried to rewrite that as (a^2 + b^2)^2 +c^4 = 4(a^2b^2 + a^2c^2 +
b^2c^2). Didn't get anywhere.
Also tried 2a^2b^2 + a^4 + b^4 = -c^4 + 2a^2c^2 + 2b^2c^2, getting
(a^2 + b^2)^2 + 2a^2b^2 = c^3 ( -c -1 ). Stuck again.

Please, set me on the right track.


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