x^4+3*x^2-2*x+5=0 (уравнение)

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    Найду корень уравнения: x^4+3*x^2-2*x+5=0

    Решение

    Вы ввели [src]
     4      2              
    x  + 3*x  - 2*x + 5 = 0
    $$- 2 x + x^{4} + 3 x^{2} + 5 = 0$$
    График
    Быстрый ответ [src]
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                                                                                                    /            /    17   I*\/ 3273                                        4                                                   23             
                                                                                      I*           /    4 + 2*3 /   - -- + ----------  + ------------------------------------------------------------------------ + -------------------------- 
                     ______________________________________________________________               /           \/      8        36                  ______________________________________________________________          ___________________ 
                    /             ___________________                                            /                                                /             ___________________                                       /            ______  
                   /             /            ______                                            /                                                /             /            ______                                       /    17   I*\/ 3273   
                  /             /    17   I*\/ 3273                 23                         /                                                /             /    17   I*\/ 3273                 23                6*3 /   - -- + ----------  
                 /    -2 + 2*3 /   - -- + ----------  + --------------------------            /                                                /    -2 + 2*3 /   - -- + ----------  + --------------------------      \/      8        36      
                /            \/      8        36               ___________________           /                                                /            \/      8        36               ___________________                               
               /                                              /            ______           /                                                /                                              /            ______                                
              /                                              /    17   I*\/ 3273           /                                                /                                              /    17   I*\/ 3273                                 
             /                                          6*3 /   - -- + ----------         /                                                /                                          6*3 /   - -- + ----------                                
           \/                                             \/      8        36           \/                                               \/                                             \/      8        36                                    
    x1 = - ------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------
                                              2                                                                                                                   2                                                                            
    $$x_{1} = - \frac{i}{2} \sqrt{4 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + \frac{4}{\sqrt{-2 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} - \frac{1}{2} \sqrt{-2 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}}$$
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                                                                                                  /                                          4                                            /    17   I*\/ 3273                 23             
                                                                                    I*           /    4 - ------------------------------------------------------------------------ + 2*3 /   - -- + ----------  + -------------------------- 
                   ______________________________________________________________               /                   ______________________________________________________________     \/      8        36               ___________________ 
                  /             ___________________                                            /                   /             ___________________                                                                    /            ______  
                 /             /            ______                                            /                   /             /            ______                                                                    /    17   I*\/ 3273   
                /             /    17   I*\/ 3273                 23                         /                   /             /    17   I*\/ 3273                 23                                             6*3 /   - -- + ----------  
               /    -2 + 2*3 /   - -- + ----------  + --------------------------            /                   /    -2 + 2*3 /   - -- + ----------  + --------------------------                                   \/      8        36      
              /            \/      8        36               ___________________           /                   /            \/      8        36               ___________________                                                            
             /                                              /            ______           /                   /                                              /            ______                                                             
            /                                              /    17   I*\/ 3273           /                   /                                              /    17   I*\/ 3273                                                              
           /                                          6*3 /   - -- + ----------         /                   /                                          6*3 /   - -- + ----------                                                             
         \/                                             \/      8        36           \/                  \/                                             \/      8        36                                                                 
    x2 = ------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------
                                            2                                                                                                                   2                                                                            
    $$x_{2} = - \frac{i}{2} \sqrt{4 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} - \frac{4}{\sqrt{-2 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + \frac{1}{2} \sqrt{-2 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}}$$
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                                                                                                     /            /            ______                                                                                                          
                                                                                                    /            /    17   I*\/ 3273                                        4                                                   23             
                                                                                      I*           /    4 + 2*3 /   - -- + ----------  + ------------------------------------------------------------------------ + -------------------------- 
                     ______________________________________________________________               /           \/      8        36                  ______________________________________________________________          ___________________ 
                    /             ___________________                                            /                                                /             ___________________                                       /            ______  
                   /             /            ______                                            /                                                /             /            ______                                       /    17   I*\/ 3273   
                  /             /    17   I*\/ 3273                 23                         /                                                /             /    17   I*\/ 3273                 23                6*3 /   - -- + ----------  
                 /    -2 + 2*3 /   - -- + ----------  + --------------------------            /                                                /    -2 + 2*3 /   - -- + ----------  + --------------------------      \/      8        36      
                /            \/      8        36               ___________________           /                                                /            \/      8        36               ___________________                               
               /                                              /            ______           /                                                /                                              /            ______                                
              /                                              /    17   I*\/ 3273           /                                                /                                              /    17   I*\/ 3273                                 
             /                                          6*3 /   - -- + ----------         /                                                /                                          6*3 /   - -- + ----------                                
           \/                                             \/      8        36           \/                                               \/                                             \/      8        36                                    
    x3 = - ------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------
                                              2                                                                                                                   2                                                                            
    $$x_{3} = - \frac{1}{2} \sqrt{-2 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + \frac{i}{2} \sqrt{4 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + \frac{4}{\sqrt{-2 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}}$$
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                                                                                                    /                                                                                       ___________________                              
                                                                                                   /                                                                                       /            ______                               
                                                                                                  /                                          4                                            /    17   I*\/ 3273                 23             
                                                                                    I*           /    4 - ------------------------------------------------------------------------ + 2*3 /   - -- + ----------  + -------------------------- 
                   ______________________________________________________________               /                   ______________________________________________________________     \/      8        36               ___________________ 
                  /             ___________________                                            /                   /             ___________________                                                                    /            ______  
                 /             /            ______                                            /                   /             /            ______                                                                    /    17   I*\/ 3273   
                /             /    17   I*\/ 3273                 23                         /                   /             /    17   I*\/ 3273                 23                                             6*3 /   - -- + ----------  
               /    -2 + 2*3 /   - -- + ----------  + --------------------------            /                   /    -2 + 2*3 /   - -- + ----------  + --------------------------                                   \/      8        36      
              /            \/      8        36               ___________________           /                   /            \/      8        36               ___________________                                                            
             /                                              /            ______           /                   /                                              /            ______                                                             
            /                                              /    17   I*\/ 3273           /                   /                                              /    17   I*\/ 3273                                                              
           /                                          6*3 /   - -- + ----------         /                   /                                          6*3 /   - -- + ----------                                                             
         \/                                             \/      8        36           \/                  \/                                             \/      8        36                                                                 
    x4 = ------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------
                                            2                                                                                                                   2                                                                            
    $$x_{4} = \frac{1}{2} \sqrt{-2 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + \frac{i}{2} \sqrt{4 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} - \frac{4}{\sqrt{-2 + \frac{23}{6 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}}} + 2 \sqrt[3]{- \frac{17}{8} + \frac{\sqrt{3273} i}{36}}}$$
    Численный ответ [src]
    x1 = 0.656576627393 + 1.08146527025*i
    x2 = -0.656576627393 + 1.64092004818*i
    x3 = -0.656576627393 - 1.64092004818*i
    x4 = 0.656576627393 - 1.08146527025*i
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