Find real numbers A,B,C,D and E that satisfy this system of equations:

(A-B+C)² = B(D+E-B), and:
(B-C+D)² = C(E+A-C), and:
(C-D+E)² = D(A+B-D), and:
(D-E+A)² = E(B+C-E), and:
(E-A+B)² = A(C+D-A)

I tried a few cases assuming two of the variables were equal and kept coming to the conclusion that all five were then equal.  So I suspect the trivial solution is the only solution.

Posted by Brian Smith on 2016-07-10 19:52:38