It is given that A,B,C and D are roots of the quartic equation X^4 - X +2 = 0. Determine, whether or not (AB+CD) is a root of the equation X^3 – 8X –1 = 0.

To adequately explain what is going on in this problem requires exceptional mathematical talent, I think.  This is because research shows that the mathematical theory behind this was discovered by  very famous classical mathematicians who preceded Galois.  Hence I class this as a "research" problem because I doubt that any perplexus visitor would ever find this theory on his or her own.  Once having done the research and found the theory that applies, it is a simple matter to verify that the two equations fit together in the way described, but this isn't "solving" the problem.

Edited on December 23, 2005, 4:02 pm

Posted by Richard on 2005-12-23 14:50:25