Nonlinear equations

 

In Mathematica

For comparison with other CAS choose from: Axiom Derive Macsyma Maple Reduce

inputs outputs

• using decompositioni for solving high degree polynomials

      Solve[ x^8 - 8x^7 + 34x^6 - 92x^5 + 175x^4 - 236x^3 +
             226x^2 - 140x + 46 == 0 ]
  

             4 - Sqrt[16 - 8 (5 - Sqrt[-3 - 4 Sqrt[3]])]
      {{x -> -------------------------------------------},
                                  4
  
             4 + Sqrt[16 - 8 (5 - Sqrt[-3 - 4 Sqrt[3]])]
       {x -> -------------------------------------------},
                                  4
  
             4 - Sqrt[16 - 8 (5 + Sqrt[-3 - 4 Sqrt[3]])]
       {x -> -------------------------------------------},
                                  4
  
             4 + Sqrt[16 - 8 (5 + Sqrt[-3 - 4 Sqrt[3]])]
       {x -> -------------------------------------------},
                                  4
  
             4 - Sqrt[16 - 8 (5 - Sqrt[-3 + 4 Sqrt[3]])]
       {x -> -------------------------------------------},
                                  4
  
             4 + Sqrt[16 - 8 (5 - Sqrt[-3 + 4 Sqrt[3]])]
       {x -> -------------------------------------------},
                                  4
  
             4 - Sqrt[16 - 8 (5 + Sqrt[-3 + 4 Sqrt[3]])]
       {x -> -------------------------------------------},
                                  4
  
             4 + Sqrt[16 - 8 (5 + Sqrt[-3 + 4 Sqrt[3]])]
       {x -> -------------------------------------------}}
                                  4

• multiple use of inversion functions

      Solve[ Log[ ArcCos[ ArcSin[x^(2/3)-b]- 1]]+ 2 == 0, x ]
  

                    3      2              -2
      {{x -> -Sqrt[b  + 3 b  Sin[1 + Cos[E  ]] +
  
                             -2  2                -2  3
            3 b Sin[1 + Cos[E  ]]  + Sin[1 + Cos[E  ]] ]},
  
                   3      2              -2
       {x -> Sqrt[b  + 3 b  Sin[1 + Cos[E  ]] +
  
                            -2  2                -2  3
           3 b Sin[1 + Cos[E  ]]  + Sin[1 + Cos[E  ]] ]}}

  
      Simplify[%]
  

                                   1   2  3
      {{x -> -Sqrt[(b + Sin[2 Cos[----] ]) ]},
                                     2
                                  2 E
  
                                  1   2  3
       {x -> Sqrt[(b + Sin[2 Cos[----] ]) ]}}
                                    2
                                 2 E