System of 3 equations 1 x + 1 y + z = a 1 y + 1 x + z = b 1 z + 1 x + y = c

Question

System of 3 equations      1          x        +      1          y      +      z        =  a        1          y        +      1          x      +      z        =  b        1          z        +      1          x      +      y        =  c

Erik Rivera · Accepted Answer

This is an old question, but for the benefit of those who&#039;ll come across this and left hanging.If   b  =  c, then there is an analytic solution which involves an octic that factors into quartics over       2  .Let   x  ,  y  ,  z  =      p    2    ,        q    2    ,        r    2   and, to avoid the octic, let   a  =      2      a. We get,                              1          p                +                  1                                    q              2                        +                          r              2                                                                  =                  2                        a                                      1          q                +                  1                                    p              2                        +                          r              2                                                                  =        b                                      1          r                +                  1                                    p              2                        +                          q              2                                                                  =        b            and the solution,  p  =            (      r      +      2      a              r        2            )              2                    4              a        2                    r        2            −      1        ,    q  =  r

System of 3 equations 1 <msqrt> x </msqrt> </mfrac> + 1 <msqrt

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