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Three Equation System Settlement (Posted on 20161007) 

Find all possible real number solutions to this system of equations:
A+B*C = B+C*A = C+A*B = 1980
I hear 'cycles'

 Comment 3 of 5 

If
A = B: A(1
+ C) = C + A^{2} = 1980
Eliminating C: A^{3}  1981A + 1980 = 0,
(A –
1)(A – 44)(A + 45) = 0
with solutions: (A, B, C) = (1, 1,
1979), (44, 44, 44), (45, 45, 45).
The first result can be cycled to obtain (1, 1979, 1) & (1979, 1, 1).

Otherwise, by analysis:
If A and B are not equal: C = 1 so A + B
= 1 + AB = 1980
Eliminating B: A^{2}  1980A + 1979 = 0
(A –
1)(A – 1979) = 0
with solutions: (A, B, C) = (1, 1979,
1), (1979, 1, 1).

Posted by Harry
on 20161010 16:51:23 


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