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)

Any values where
A=B=C=D=E
make the equations all become
A²=A²
so there's one infinite class of solutions.

There may be others but if so I haven't found the trick.

Posted by Jer on 2015-12-20 15:48:24