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Respuesta:
Date: 11/08/2001 at 17:12:29
From: Doctor Greenie
Subject: Re: Advanced Algebra
Hello, Phil -
I have seen problems like this before, but I have never taken the time
to try to finish working one of them out to the end. Having had some
free time since I first saw this question of yours, I have solved this
problem - not just your specific case, but the general case. Thanks
for sending the question; it gave me a lot of good (and enjoyable)
mental exercise.
I'll present my solution roughly as I was able to figure it out. The
actual path I took to the solution was more convoluted than the
presentation below; I have cleaned things up a bit.
We start with
(1) a+b+c = 3
(2) a^2+b^2+c^2 = 5
(3) a^3+b^3+c^3 = 7
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