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Elana
Posts:
22
Registered:
12/6/04
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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.
Elana
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