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  • Equation:
  • 3*(2*x+10)=0
  • (x2-25)/(y+1)=0
  • (x^2+5*x)/(x-4)=0
  • 8-2x=0
  • Identical expressions

  • six *x^ four -x^ three + five *x^ two - one = zero
  • 6 multiply by x to the power of 4 minus x cubed plus 5 multiply by x squared minus 1 equally 0
  • six multiply by x to the power of four minus x to the power of three plus five multiply by x to the power of two minus one equally zero
  • 6*x4-x3+5*x2-1=0
  • 6*x⁴-x³+5*x²-1=0
  • 6*x to the power of 4-x to the power of 3+5*x to the power of 2-1=0
  • 6x^4-x^3+5x^2-1=0
  • 6x4-x3+5x2-1=0
  • 6*x^4-x^3+5*x^2-1=O
  • Similar expressions

  • 6*x^4-x^3+5*x^2+1=0
  • 6*x^4+x^3+5*x^2-1=0
  • 6*x^4-x^3-5*x^2-1=0

6*x^4-x^3+5*x^2-1=0 equation

A equation with variable:

Numerical solution:

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The solution

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   4    3      2        
6*x  - x  + 5*x  - 1 = 0
$$\left(5 x^{2} + \left(6 x^{4} - x^{3}\right)\right) - 1 = 0$$
The graph
Rapid solution [src]
                         __________________________________________________________________________________________________________________________________________________________                                                                                  
                        /               ____________________                                                                                                                                                                                                         
                       /               /           ________                                                                                                                                                                                                          
                      /     79        /   2383   \/ 677109                   47                                                        119                                                                                                                           
                     /    - -- - 2*3 /   ----- + ----------  + ----------------------------- + -----------------------------------------------------------------------------------                                                                                   
                    /       72     \/    93312     31104                ____________________                 _____________________________________________________________________              _____________________________________________________________________
                   /                                                   /           ________                 /                ____________________                                              /                ____________________                                 
                  /                                                   /   2383   \/ 677109                 /                /           ________                                              /                /           ________                                  
                 /                                             648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47                         /      79        /   2383   \/ 677109                   47              
                /                                                  \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------           /    - --- + 2*3 /   ----- + ----------  - ----------------------------- 
               /                                                                                        /       144     \/    93312     31104                ____________________          /       144     \/    93312     31104                ____________________ 
              /                                                                                        /                                                    /           ________          /                                                    /           ________  
             /                                                                                        /                                                    /   2383   \/ 677109          /                                                    /   2383   \/ 677109   
            /                                                                                        /                                              648*3 /   ----- + ----------        /                                              648*3 /   ----- + ----------  
     1    \/                                                                                       \/                                                   \/    93312     31104         \/                                                   \/    93312     31104     
x1 = -- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------
     24                                                                                       2                                                                                                                              2                                       
$$x_{1} = - \frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24} + \frac{\sqrt{- \frac{79}{72} - 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2}$$
                                                                                                           __________________________________________________________________________________________________________________________________________________________
                                                                                                          /               ____________________                                                                                                                       
                                                                                                         /               /           ________                                                                                                                        
                                                                                                        /     79        /   2383   \/ 677109                   47                                                        119                                         
                                                                                                       /    - -- - 2*3 /   ----- + ----------  + ----------------------------- + ----------------------------------------------------------------------------------- 
                    _____________________________________________________________________             /       72     \/    93312     31104                ____________________                 _____________________________________________________________________ 
                   /                ____________________                                             /                                                   /           ________                 /                ____________________                                  
                  /                /           ________                                             /                                                   /   2383   \/ 677109                 /                /           ________                                   
                 /      79        /   2383   \/ 677109                   47                        /                                             648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47               
                /    - --- + 2*3 /   ----- + ----------  - -----------------------------          /                                                  \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------  
               /       144     \/    93312     31104                ____________________         /                                                                                        /       144     \/    93312     31104                ____________________  
              /                                                    /           ________         /                                                                                        /                                                    /           ________   
             /                                                    /   2383   \/ 677109         /                                                                                        /                                                    /   2383   \/ 677109    
            /                                              648*3 /   ----- + ----------       /                                                                                        /                                              648*3 /   ----- + ----------   
     1    \/                                                   \/    93312     31104        \/                                                                                       \/                                                   \/    93312     31104      
x2 = -- - ------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------
     24                                          2                                                                                                                              2                                                                                    
$$x_{2} = - \frac{\sqrt{- \frac{79}{72} - 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2} - \frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24}$$
                                                                                                             ________________________________________________________________________________________________________________________________________________________
                                                                                                            /             ____________________                                                                                                                       
                                                                                                           /             /           ________                                                                                                                        
                                                                                                          /   79        /   2383   \/ 677109                   47                                                        119                                         
                                                                                            I*           /    -- + 2*3 /   ----- + ----------  - ----------------------------- + ----------------------------------------------------------------------------------- 
                    _____________________________________________________________________               /     72     \/    93312     31104                ____________________                 _____________________________________________________________________ 
                   /                ____________________                                               /                                                 /           ________                 /                ____________________                                  
                  /                /           ________                                               /                                                 /   2383   \/ 677109                 /                /           ________                                   
                 /      79        /   2383   \/ 677109                   47                          /                                           648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47               
                /    - --- + 2*3 /   ----- + ----------  - -----------------------------            /                                                \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------  
               /       144     \/    93312     31104                ____________________           /                                                                                      /       144     \/    93312     31104                ____________________  
              /                                                    /           ________           /                                                                                      /                                                    /           ________   
             /                                                    /   2383   \/ 677109           /                                                                                      /                                                    /   2383   \/ 677109    
            /                                              648*3 /   ----- + ----------         /                                                                                      /                                              648*3 /   ----- + ----------   
     1    \/                                                   \/    93312     31104          \/                                                                                     \/                                                   \/    93312     31104      
x3 = -- + ------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------
     24                                          2                                                                                                                              2                                                                                    
$$x_{3} = \frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24} - \frac{i \sqrt{- \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{79}{72} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2}$$
                                                                                                             ________________________________________________________________________________________________________________________________________________________
                                                                                                            /             ____________________                                                                                                                       
                                                                                                           /             /           ________                                                                                                                        
                                                                                                          /   79        /   2383   \/ 677109                   47                                                        119                                         
                                                                                            I*           /    -- + 2*3 /   ----- + ----------  - ----------------------------- + ----------------------------------------------------------------------------------- 
                    _____________________________________________________________________               /     72     \/    93312     31104                ____________________                 _____________________________________________________________________ 
                   /                ____________________                                               /                                                 /           ________                 /                ____________________                                  
                  /                /           ________                                               /                                                 /   2383   \/ 677109                 /                /           ________                                   
                 /      79        /   2383   \/ 677109                   47                          /                                           648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47               
                /    - --- + 2*3 /   ----- + ----------  - -----------------------------            /                                                \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------  
               /       144     \/    93312     31104                ____________________           /                                                                                      /       144     \/    93312     31104                ____________________  
              /                                                    /           ________           /                                                                                      /                                                    /           ________   
             /                                                    /   2383   \/ 677109           /                                                                                      /                                                    /   2383   \/ 677109    
            /                                              648*3 /   ----- + ----------         /                                                                                      /                                              648*3 /   ----- + ----------   
     1    \/                                                   \/    93312     31104          \/                                                                                     \/                                                   \/    93312     31104      
x4 = -- + ------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------
     24                                          2                                                                                                                              2                                                                                    
$$x_{4} = \frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24} + \frac{i \sqrt{- \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{79}{72} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2}$$
x4 = sqrt(-79/144 - 47/(648*(2383/93312 + sqrt(677109)/31104)^(1/3)) + 2*(2383/93312 + sqrt(677109)/31104)^(1/3))/2 + 1/24 + i*sqrt(-47/(648*(2383/93312 + sqrt(677109)/31104)^(1/3)) + 2*(2383/93312 + sqrt(677109)/31104)^(1/3) + 79/72 + 119/(864*sqrt(-79/144 - 47/(648*(2383/93312 + sqrt(677109)/31104)^(1/3)) + 2*(2383/93312 + sqrt(677109)/31104)^(1/3))))/2
Sum and product of roots [src]
sum
                    __________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                           __________________________________________________________________________________________________________________________________________________________                                                                                                           ________________________________________________________________________________________________________________________________________________________                                                                                                           ________________________________________________________________________________________________________________________________________________________
                   /               ____________________                                                                                                                                                                                                                                                                                                                 /               ____________________                                                                                                                                                                                                                                 /             ____________________                                                                                                                                                                                                                                 /             ____________________                                                                                                                       
                  /               /           ________                                                                                                                                                                                                                                                                                                                 /               /           ________                                                                                                                                                                                                                                 /             /           ________                                                                                                                                                                                                                                 /             /           ________                                                                                                                        
                 /     79        /   2383   \/ 677109                   47                                                        119                                                                                                                                                                                                                                 /     79        /   2383   \/ 677109                   47                                                        119                                                                                                                                                 /   79        /   2383   \/ 677109                   47                                                        119                                                                                                                                                 /   79        /   2383   \/ 677109                   47                                                        119                                         
                /    - -- - 2*3 /   ----- + ----------  + ----------------------------- + -----------------------------------------------------------------------------------                                                                                                                                                                                        /    - -- - 2*3 /   ----- + ----------  + ----------------------------- + -----------------------------------------------------------------------------------                                                                                           I*           /    -- + 2*3 /   ----- + ----------  - ----------------------------- + -----------------------------------------------------------------------------------                                                                                           I*           /    -- + 2*3 /   ----- + ----------  - ----------------------------- + ----------------------------------------------------------------------------------- 
               /       72     \/    93312     31104                ____________________                 _____________________________________________________________________              _____________________________________________________________________                  _____________________________________________________________________             /       72     \/    93312     31104                ____________________                 _____________________________________________________________________                   _____________________________________________________________________               /     72     \/    93312     31104                ____________________                 _____________________________________________________________________                   _____________________________________________________________________               /     72     \/    93312     31104                ____________________                 _____________________________________________________________________ 
              /                                                   /           ________                 /                ____________________                                              /                ____________________                                                  /                ____________________                                             /                                                   /           ________                 /                ____________________                                                   /                ____________________                                               /                                                 /           ________                 /                ____________________                                                   /                ____________________                                               /                                                 /           ________                 /                ____________________                                  
             /                                                   /   2383   \/ 677109                 /                /           ________                                              /                /           ________                                                  /                /           ________                                             /                                                   /   2383   \/ 677109                 /                /           ________                                                   /                /           ________                                               /                                                 /   2383   \/ 677109                 /                /           ________                                                   /                /           ________                                               /                                                 /   2383   \/ 677109                 /                /           ________                                   
            /                                             648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47                         /      79        /   2383   \/ 677109                   47                             /      79        /   2383   \/ 677109                   47                        /                                             648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47                              /      79        /   2383   \/ 677109                   47                          /                                           648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47                              /      79        /   2383   \/ 677109                   47                          /                                           648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47               
           /                                                  \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------           /    - --- + 2*3 /   ----- + ----------  - -----------------------------               /    - --- + 2*3 /   ----- + ----------  - -----------------------------          /                                                  \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------                /    - --- + 2*3 /   ----- + ----------  - -----------------------------            /                                                \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------                /    - --- + 2*3 /   ----- + ----------  - -----------------------------            /                                                \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------  
          /                                                                                        /       144     \/    93312     31104                ____________________          /       144     \/    93312     31104                ____________________              /       144     \/    93312     31104                ____________________         /                                                                                        /       144     \/    93312     31104                ____________________               /       144     \/    93312     31104                ____________________           /                                                                                      /       144     \/    93312     31104                ____________________               /       144     \/    93312     31104                ____________________           /                                                                                      /       144     \/    93312     31104                ____________________  
         /                                                                                        /                                                    /           ________          /                                                    /           ________              /                                                    /           ________         /                                                                                        /                                                    /           ________               /                                                    /           ________           /                                                                                      /                                                    /           ________               /                                                    /           ________           /                                                                                      /                                                    /           ________   
        /                                                                                        /                                                    /   2383   \/ 677109          /                                                    /   2383   \/ 677109              /                                                    /   2383   \/ 677109         /                                                                                        /                                                    /   2383   \/ 677109               /                                                    /   2383   \/ 677109           /                                                                                      /                                                    /   2383   \/ 677109               /                                                    /   2383   \/ 677109           /                                                                                      /                                                    /   2383   \/ 677109    
       /                                                                                        /                                              648*3 /   ----- + ----------        /                                              648*3 /   ----- + ----------            /                                              648*3 /   ----- + ----------       /                                                                                        /                                              648*3 /   ----- + ----------             /                                              648*3 /   ----- + ----------         /                                                                                      /                                              648*3 /   ----- + ----------             /                                              648*3 /   ----- + ----------         /                                                                                      /                                              648*3 /   ----- + ----------   
1    \/                                                                                       \/                                                   \/    93312     31104         \/                                                   \/    93312     31104        1    \/                                                   \/    93312     31104        \/                                                                                       \/                                                   \/    93312     31104         1    \/                                                   \/    93312     31104          \/                                                                                     \/                                                   \/    93312     31104         1    \/                                                   \/    93312     31104          \/                                                                                     \/                                                   \/    93312     31104      
-- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------- + -- - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -- + ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -- + ------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------
24                                                                                       2                                                                                                                              2                                          24                                          2                                                                                                                              2                                                                                       24                                          2                                                                                                                              2                                                                                       24                                          2                                                                                                                              2                                                                                    
$$\left(\left(\left(- \frac{\sqrt{- \frac{79}{72} - 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2} - \frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24}\right) + \left(- \frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24} + \frac{\sqrt{- \frac{79}{72} - 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2}\right)\right) + \left(\frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24} - \frac{i \sqrt{- \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{79}{72} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2}\right)\right) + \left(\frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24} + \frac{i \sqrt{- \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{79}{72} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2}\right)$$
=
1/6
$$\frac{1}{6}$$
product
/                    __________________________________________________________________________________________________________________________________________________________                                                                                  \ /                                                                                                      __________________________________________________________________________________________________________________________________________________________\ /                                                                                                        ________________________________________________________________________________________________________________________________________________________\ /                                                                                                        ________________________________________________________________________________________________________________________________________________________\
|                   /               ____________________                                                                                                                                                                                                         | |                                                                                                     /               ____________________                                                                                                                       | |                                                                                                       /             ____________________                                                                                                                       | |                                                                                                       /             ____________________                                                                                                                       |
|                  /               /           ________                                                                                                                                                                                                          | |                                                                                                    /               /           ________                                                                                                                        | |                                                                                                      /             /           ________                                                                                                                        | |                                                                                                      /             /           ________                                                                                                                        |
|                 /     79        /   2383   \/ 677109                   47                                                        119                                                                                                                           | |                                                                                                   /     79        /   2383   \/ 677109                   47                                                        119                                         | |                                                                                                     /   79        /   2383   \/ 677109                   47                                                        119                                         | |                                                                                                     /   79        /   2383   \/ 677109                   47                                                        119                                         |
|                /    - -- - 2*3 /   ----- + ----------  + ----------------------------- + -----------------------------------------------------------------------------------                                                                                   | |                                                                                                  /    - -- - 2*3 /   ----- + ----------  + ----------------------------- + ----------------------------------------------------------------------------------- | |                                                                                       I*           /    -- + 2*3 /   ----- + ----------  - ----------------------------- + ----------------------------------------------------------------------------------- | |                                                                                       I*           /    -- + 2*3 /   ----- + ----------  - ----------------------------- + ----------------------------------------------------------------------------------- |
|               /       72     \/    93312     31104                ____________________                 _____________________________________________________________________              _____________________________________________________________________| |               _____________________________________________________________________             /       72     \/    93312     31104                ____________________                 _____________________________________________________________________ | |               _____________________________________________________________________               /     72     \/    93312     31104                ____________________                 _____________________________________________________________________ | |               _____________________________________________________________________               /     72     \/    93312     31104                ____________________                 _____________________________________________________________________ |
|              /                                                   /           ________                 /                ____________________                                              /                ____________________                                 | |              /                ____________________                                             /                                                   /           ________                 /                ____________________                                  | |              /                ____________________                                               /                                                 /           ________                 /                ____________________                                  | |              /                ____________________                                               /                                                 /           ________                 /                ____________________                                  |
|             /                                                   /   2383   \/ 677109                 /                /           ________                                              /                /           ________                                  | |             /                /           ________                                             /                                                   /   2383   \/ 677109                 /                /           ________                                   | |             /                /           ________                                               /                                                 /   2383   \/ 677109                 /                /           ________                                   | |             /                /           ________                                               /                                                 /   2383   \/ 677109                 /                /           ________                                   |
|            /                                             648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47                         /      79        /   2383   \/ 677109                   47              | |            /      79        /   2383   \/ 677109                   47                        /                                             648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47               | |            /      79        /   2383   \/ 677109                   47                          /                                           648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47               | |            /      79        /   2383   \/ 677109                   47                          /                                           648*3 /   ----- + ----------               /      79        /   2383   \/ 677109                   47               |
|           /                                                  \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------           /    - --- + 2*3 /   ----- + ----------  - ----------------------------- | |           /    - --- + 2*3 /   ----- + ----------  - -----------------------------          /                                                  \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------  | |           /    - --- + 2*3 /   ----- + ----------  - -----------------------------            /                                                \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------  | |           /    - --- + 2*3 /   ----- + ----------  - -----------------------------            /                                                \/    93312     31104       864*      /    - --- + 2*3 /   ----- + ----------  - -----------------------------  |
|          /                                                                                        /       144     \/    93312     31104                ____________________          /       144     \/    93312     31104                ____________________ | |          /       144     \/    93312     31104                ____________________         /                                                                                        /       144     \/    93312     31104                ____________________  | |          /       144     \/    93312     31104                ____________________           /                                                                                      /       144     \/    93312     31104                ____________________  | |          /       144     \/    93312     31104                ____________________           /                                                                                      /       144     \/    93312     31104                ____________________  |
|         /                                                                                        /                                                    /           ________          /                                                    /           ________  | |         /                                                    /           ________         /                                                                                        /                                                    /           ________   | |         /                                                    /           ________           /                                                                                      /                                                    /           ________   | |         /                                                    /           ________           /                                                                                      /                                                    /           ________   |
|        /                                                                                        /                                                    /   2383   \/ 677109          /                                                    /   2383   \/ 677109   | |        /                                                    /   2383   \/ 677109         /                                                                                        /                                                    /   2383   \/ 677109    | |        /                                                    /   2383   \/ 677109           /                                                                                      /                                                    /   2383   \/ 677109    | |        /                                                    /   2383   \/ 677109           /                                                                                      /                                                    /   2383   \/ 677109    |
|       /                                                                                        /                                              648*3 /   ----- + ----------        /                                              648*3 /   ----- + ----------  | |       /                                              648*3 /   ----- + ----------       /                                                                                        /                                              648*3 /   ----- + ----------   | |       /                                              648*3 /   ----- + ----------         /                                                                                      /                                              648*3 /   ----- + ----------   | |       /                                              648*3 /   ----- + ----------         /                                                                                      /                                              648*3 /   ----- + ----------   |
|1    \/                                                                                       \/                                                   \/    93312     31104         \/                                                   \/    93312     31104     | |1    \/                                                   \/    93312     31104        \/                                                                                       \/                                                   \/    93312     31104      | |1    \/                                                   \/    93312     31104          \/                                                                                     \/                                                   \/    93312     31104      | |1    \/                                                   \/    93312     31104          \/                                                                                     \/                                                   \/    93312     31104      |
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\24                                                                                       2                                                                                                                              2                                       / \24                                          2                                                                                                                              2                                                                                    / \24                                          2                                                                                                                              2                                                                                    / \24                                          2                                                                                                                              2                                                                                    /
$$\left(- \frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24} + \frac{\sqrt{- \frac{79}{72} - 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2}\right) \left(- \frac{\sqrt{- \frac{79}{72} - 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2} - \frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24}\right) \left(\frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24} - \frac{i \sqrt{- \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{79}{72} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2}\right) \left(\frac{\sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}{2} + \frac{1}{24} + \frac{i \sqrt{- \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}} + \frac{79}{72} + \frac{119}{864 \sqrt{- \frac{79}{144} - \frac{47}{648 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}} + 2 \sqrt[3]{\frac{2383}{93312} + \frac{\sqrt{677109}}{31104}}}}}}{2}\right)$$
=
-1/6
$$- \frac{1}{6}$$
-1/6
Numerical answer [src]
x1 = 0.42098669378684
x2 = 0.0713686352156971 + 0.995981964434728*i
x3 = 0.0713686352156971 - 0.995981964434728*i
x4 = -0.397057297551568
x4 = -0.397057297551568
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