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Three Equation System Settlement (Posted on 2016-10-07) Difficulty: 3 of 5
Find all possible real number solutions to this system of equations:

A+B*C = B+C*A = C+A*B = 1980

No Solution Yet Submitted by K Sengupta    
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Solution I hear 'cycles' | Comment 3 of 5 |
If A = B:                       A(1 + C) = C + A2 = 1980

            Eliminating C:    A3 - 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).
           
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Otherwise, by analysis:

If A and B are not equal: C = 1 so  A + B = 1 + AB = 1980

            Eliminating B:    A2 - 1980A + 1979 = 0

                                    (A – 1)(A – 1979) = 0

with solutions:  (A, B, C) = (1, 1979, 1), (1979, 1, 1).



  Posted by Harry on 2016-10-10 16:51:23
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