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Quadratic and Five Variable Query (Posted on 2015-12-20) Difficulty: 3 of 5
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)

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Thoughts Comment 2 of 2 |
By adding all the equations together and simplifying I got the result:
A^2+B^2+C^2+D^2+E^2 = A*B+B*C+C*D+D*E+E*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
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