Determine all possible real solutions to this system of equations:

A+B+C+D = 5, and:
A*B+B*C+C*D+D*A = 4, and:
A*B*C+B*C*D+C*D*A+D*A*B= 3, and:
A*B*C*D= -1

Prove that there are no others.

(In reply to adding on by xdog)

Well spotted xdog. This will avoid the need for the quartic equation. But I've a feeling  that no further real solutions will emerge.

Posted by Harry on 2016-08-12 06:13:25