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x^5+x+2=0 (уравнение)

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    Найду корень уравнения: x^5+x+2=0

    Решение

    Вы ввели [src]
     5            
x  + x + 2 = 0
    $$x^{5} + x + 2 = 0$$
    График
    Быстрый ответ [src]
    x1 = -1
    $$x_{1} = -1$$
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                                                                                                       /            /             ______                                                                                                                 
                                                                                                      /   5        /     35   I*\/ 1047                                           5                                                       11             
                                                                                        I*           /    - + 2*3 /   - --- + ----------  + ------------------------------------------------------------------------------ + --------------------------- 
                   __________________________________________________________________               /     6     \/      216       72                    __________________________________________________________________          ____________________ 
                  /               ____________________                                             /                                                   /               ____________________                                        /             ______  
                 /               /             ______                                             /                                                   /               /             ______                                        /     35   I*\/ 1047   
                /     5         /     35   I*\/ 1047                  11                         /                                                   /     5         /     35   I*\/ 1047                  11                9*3 /   - --- + ----------  
               /    - -- + 2*3 /   - --- + ----------  + ---------------------------            /                                           4*      /    - -- + 2*3 /   - --- + ----------  + ---------------------------      \/      216       72      
              /       12     \/      216       72               ____________________           /                                                   /       12     \/      216       72               ____________________                                
             /                                                 /             ______           /                                                   /                                                 /             ______                                 
            /                                                 /     35   I*\/ 1047           /                                                   /                                                 /     35   I*\/ 1047                                  
           /                                             9*3 /   - --- + ----------         /                                                   /                                             9*3 /   - --- + ----------                                 
     1   \/                                                \/      216       72           \/                                                  \/                                                \/      216       72                                     
x2 = - - ---------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------
     4                                        2                                                                                                                         2
    $$x_{2} = \frac{1}{4} - \frac{i}{2} \sqrt{\frac{5}{6} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + \frac{5}{4 \sqrt{- \frac{5}{12} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} - \frac{1}{2} \sqrt{- \frac{5}{12} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}}$$
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                                                                                                       /            /             ______                                                                                                                 
                                                                                                      /   5        /     35   I*\/ 1047                                           5                                                       11             
                                                                                        I*           /    - + 2*3 /   - --- + ----------  - ------------------------------------------------------------------------------ + --------------------------- 
                   __________________________________________________________________               /     6     \/      216       72                    __________________________________________________________________          ____________________ 
                  /               ____________________                                             /                                                   /               ____________________                                        /             ______  
                 /               /             ______                                             /                                                   /               /             ______                                        /     35   I*\/ 1047   
                /     5         /     35   I*\/ 1047                  11                         /                                                   /     5         /     35   I*\/ 1047                  11                9*3 /   - --- + ----------  
               /    - -- + 2*3 /   - --- + ----------  + ---------------------------            /                                           4*      /    - -- + 2*3 /   - --- + ----------  + ---------------------------      \/      216       72      
              /       12     \/      216       72               ____________________           /                                                   /       12     \/      216       72               ____________________                                
             /                                                 /             ______           /                                                   /                                                 /             ______                                 
            /                                                 /     35   I*\/ 1047           /                                                   /                                                 /     35   I*\/ 1047                                  
           /                                             9*3 /   - --- + ----------         /                                                   /                                             9*3 /   - --- + ----------                                 
     1   \/                                                \/      216       72           \/                                                  \/                                                \/      216       72                                     
x3 = - + ---------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------
     4                                        2                                                                                                                         2
    $$x_{3} = \frac{1}{4} - \frac{i}{2} \sqrt{\frac{5}{6} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} - \frac{5}{4 \sqrt{- \frac{5}{12} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + \frac{1}{2} \sqrt{- \frac{5}{12} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}}$$
                                                                                                             ________________________________________________________________________________________________________________________________________________
                                                                                                        /            ____________________                                                                                                                
                                                                                                       /            /             ______                                                                                                                 
                                                                                                      /   5        /     35   I*\/ 1047                                           5                                                       11             
                                                                                        I*           /    - + 2*3 /   - --- + ----------  + ------------------------------------------------------------------------------ + --------------------------- 
                   __________________________________________________________________               /     6     \/      216       72                    __________________________________________________________________          ____________________ 
                  /               ____________________                                             /                                                   /               ____________________                                        /             ______  
                 /               /             ______                                             /                                                   /               /             ______                                        /     35   I*\/ 1047   
                /     5         /     35   I*\/ 1047                  11                         /                                                   /     5         /     35   I*\/ 1047                  11                9*3 /   - --- + ----------  
               /    - -- + 2*3 /   - --- + ----------  + ---------------------------            /                                           4*      /    - -- + 2*3 /   - --- + ----------  + ---------------------------      \/      216       72      
              /       12     \/      216       72               ____________________           /                                                   /       12     \/      216       72               ____________________                                
             /                                                 /             ______           /                                                   /                                                 /             ______                                 
            /                                                 /     35   I*\/ 1047           /                                                   /                                                 /     35   I*\/ 1047                                  
           /                                             9*3 /   - --- + ----------         /                                                   /                                             9*3 /   - --- + ----------                                 
     1   \/                                                \/      216       72           \/                                                  \/                                                \/      216       72                                     
x4 = - - ---------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------
     4                                        2                                                                                                                         2
    $$x_{4} = \frac{1}{4} - \frac{1}{2} \sqrt{- \frac{5}{12} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + \frac{i}{2} \sqrt{\frac{5}{6} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + \frac{5}{4 \sqrt{- \frac{5}{12} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}}$$
                                                                                                             ________________________________________________________________________________________________________________________________________________
                                                                                                        /            ____________________                                                                                                                
                                                                                                       /            /             ______                                                                                                                 
                                                                                                      /   5        /     35   I*\/ 1047                                           5                                                       11             
                                                                                        I*           /    - + 2*3 /   - --- + ----------  - ------------------------------------------------------------------------------ + --------------------------- 
                   __________________________________________________________________               /     6     \/      216       72                    __________________________________________________________________          ____________________ 
                  /               ____________________                                             /                                                   /               ____________________                                        /             ______  
                 /               /             ______                                             /                                                   /               /             ______                                        /     35   I*\/ 1047   
                /     5         /     35   I*\/ 1047                  11                         /                                                   /     5         /     35   I*\/ 1047                  11                9*3 /   - --- + ----------  
               /    - -- + 2*3 /   - --- + ----------  + ---------------------------            /                                           4*      /    - -- + 2*3 /   - --- + ----------  + ---------------------------      \/      216       72      
              /       12     \/      216       72               ____________________           /                                                   /       12     \/      216       72               ____________________                                
             /                                                 /             ______           /                                                   /                                                 /             ______                                 
            /                                                 /     35   I*\/ 1047           /                                                   /                                                 /     35   I*\/ 1047                                  
           /                                             9*3 /   - --- + ----------         /                                                   /                                             9*3 /   - --- + ----------                                 
     1   \/                                                \/      216       72           \/                                                  \/                                                \/      216       72                                     
x5 = - + ---------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------
     4                                        2                                                                                                                         2
    $$x_{5} = \frac{1}{4} + \frac{1}{2} \sqrt{- \frac{5}{12} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + \frac{i}{2} \sqrt{\frac{5}{6} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} - \frac{5}{4 \sqrt{- \frac{5}{12} + \frac{11}{9 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}}} + 2 \sqrt[3]{- \frac{35}{216} + \frac{\sqrt{1047} i}{72}}}$$
    Численный ответ [src]
    x1 = -0.473430108465 - 1.02559058595*i
    x2 = 0.973430108465 - 0.787315815719*i
    x3 = 0.973430108465 + 0.787315815719*i
    x4 = -0.473430108465 + 1.02559058595*i
    x5 = -1.00000000000000
    График
    x^5+x+2=0 (уравнение) /media/krcore-image-pods/7e72/6f8b/9c31/ff07/im.png