Найдите сумму корней уравнения 6*40184897/(100*(x^3))+17799099/(1000*(x^2))=891*10^6 (6 умножить на 40184897 делить на (100 умножить на (х в кубе)) плюс 17799099 делить на (1000 умножить на (х в квадрате)) равно 891 умножить на 10 в степени 6) [Есть ОТВЕТ!]

Сумма корней 6*40184897/(100*(x^3))+17 ... 099/(1000*(x^2))=891*10^6

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    Решение

    Сумма и произведение корней [src]
    сумма
                                                                                      _____________________________________________________     /             _____________________________________________________                                                                           \                                                                                     _____________________________________________________     /           _____________________________________________________                                                                           \                                                                                                                                       
                                                                                     /                 ___________________________________      |            /                 ___________________________________                                                                            |                                                                                    /                 ___________________________________      |          /                 ___________________________________                                                                            |                                                                                                                                       
                                                                                    /    40184897    \/ 142442181927182540809472643836930       |    ___    /    40184897    \/ 142442181927182540809472643836930                                                                             |                                                                                   /    40184897    \/ 142442181927182540809472643836930       |  ___    /    40184897    \/ 142442181927182540809472643836930                                                                             |        _____________________________________________________                                                                          
                                                                                 3 /   ----------- + -------------------------------------      |  \/ 3 *3 /   ----------- + -------------------------------------                                           ___                              |                                                                                3 /   ----------- + -------------------------------------      |\/ 3 *3 /   ----------- + -------------------------------------                                           ___                              |       /                 ___________________________________                                                                           
                                      5933033                                    \/    29700000000            8820900000000000000               |        \/    29700000000            8820900000000000000                                          5933033*\/ 3                               |                                     5933033                                    \/    29700000000            8820900000000000000               |      \/    29700000000            8820900000000000000                                          5933033*\/ 3                               |      /    40184897    \/ 142442181927182540809472643836930                                     5933033                                
    - ------------------------------------------------------------------------ - ---------------------------------------------------------- + I*|- ---------------------------------------------------------------- + ------------------------------------------------------------------------| + - ------------------------------------------------------------------------ - ---------------------------------------------------------- + I*|---------------------------------------------------------------- - ------------------------------------------------------------------------| + 3 /   ----------- + -------------------------------------  + -----------------------------------------------------------------------
                         _____________________________________________________                               2                                  |                                 2                                                      _____________________________________________________|                        _____________________________________________________                               2                                  |                               2                                                      _____________________________________________________|   \/    29700000000            8820900000000000000                               _____________________________________________________
                        /                 ___________________________________                                                                   |                                                                                       /                 ___________________________________ |                       /                 ___________________________________                                                                   |                                                                                     /                 ___________________________________ |                                                                                 /                 ___________________________________ 
                       /    40184897    \/ 142442181927182540809472643836930                                                                    |                                                                                      /    40184897    \/ 142442181927182540809472643836930  |                      /    40184897    \/ 142442181927182540809472643836930                                                                    |                                                                                    /    40184897    \/ 142442181927182540809472643836930  |                                                                                /    40184897    \/ 142442181927182540809472643836930  
      1782000000000*3 /   ----------- + -------------------------------------                                                                   |                                                                     1782000000000*3 /   ----------- + ------------------------------------- |     1782000000000*3 /   ----------- + -------------------------------------                                                                   |                                                                   1782000000000*3 /   ----------- + ------------------------------------- |                                                                891000000000*3 /   ----------- + ------------------------------------- 
                    \/    29700000000            8820900000000000000                                                                            \                                                                                   \/    29700000000            8820900000000000000          /                   \/    29700000000            8820900000000000000                                                                            \                                                                                 \/    29700000000            8820900000000000000          /                                                                             \/    29700000000            8820900000000000000          
    $$\left(\frac{5933033}{891000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} - \frac{5933033}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} + \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} - \frac{5933033}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + i \left(- \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2}\right)\right)\right)$$
    =
      /           _____________________________________________________                                                                           \     /             _____________________________________________________                                                                           \
      |          /                 ___________________________________                                                                            |     |            /                 ___________________________________                                                                            |
      |  ___    /    40184897    \/ 142442181927182540809472643836930                                                                             |     |    ___    /    40184897    \/ 142442181927182540809472643836930                                                                             |
      |\/ 3 *3 /   ----------- + -------------------------------------                                           ___                              |     |  \/ 3 *3 /   ----------- + -------------------------------------                                           ___                              |
      |      \/    29700000000            8820900000000000000                                          5933033*\/ 3                               |     |        \/    29700000000            8820900000000000000                                          5933033*\/ 3                               |
    I*|---------------------------------------------------------------- - ------------------------------------------------------------------------| + I*|- ---------------------------------------------------------------- + ------------------------------------------------------------------------|
      |                               2                                                      _____________________________________________________|     |                                 2                                                      _____________________________________________________|
      |                                                                                     /                 ___________________________________ |     |                                                                                       /                 ___________________________________ |
      |                                                                                    /    40184897    \/ 142442181927182540809472643836930  |     |                                                                                      /    40184897    \/ 142442181927182540809472643836930  |
      |                                                                   1782000000000*3 /   ----------- + ------------------------------------- |     |                                                                     1782000000000*3 /   ----------- + ------------------------------------- |
      \                                                                                 \/    29700000000            8820900000000000000          /     \                                                                                   \/    29700000000            8820900000000000000          /
    $$i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} + \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}\right) + i \left(- \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2}\right)$$
    произведение
    /                                                                                  _____________________________________________________     /             _____________________________________________________                                                                           \\ /                                                                                  _____________________________________________________     /           _____________________________________________________                                                                           \\                                                                                                                                       
    |                                                                                 /                 ___________________________________      |            /                 ___________________________________                                                                            || |                                                                                 /                 ___________________________________      |          /                 ___________________________________                                                                            ||                                                                                                                                       
    |                                                                                /    40184897    \/ 142442181927182540809472643836930       |    ___    /    40184897    \/ 142442181927182540809472643836930                                                                             || |                                                                                /    40184897    \/ 142442181927182540809472643836930       |  ___    /    40184897    \/ 142442181927182540809472643836930                                                                             || /     _____________________________________________________                                                                          \
    |                                                                             3 /   ----------- + -------------------------------------      |  \/ 3 *3 /   ----------- + -------------------------------------                                           ___                              || |                                                                             3 /   ----------- + -------------------------------------      |\/ 3 *3 /   ----------- + -------------------------------------                                           ___                              || |    /                 ___________________________________                                                                           |
    |                                  5933033                                    \/    29700000000            8820900000000000000               |        \/    29700000000            8820900000000000000                                          5933033*\/ 3                               || |                                  5933033                                    \/    29700000000            8820900000000000000               |      \/    29700000000            8820900000000000000                                          5933033*\/ 3                               || |   /    40184897    \/ 142442181927182540809472643836930                                     5933033                                |
    |- ------------------------------------------------------------------------ - ---------------------------------------------------------- + I*|- ---------------------------------------------------------------- + ------------------------------------------------------------------------||*|- ------------------------------------------------------------------------ - ---------------------------------------------------------- + I*|---------------------------------------------------------------- - ------------------------------------------------------------------------||*|3 /   ----------- + -------------------------------------  + -----------------------------------------------------------------------|
    |                     _____________________________________________________                               2                                  |                                 2                                                      _____________________________________________________|| |                     _____________________________________________________                               2                                  |                               2                                                      _____________________________________________________|| |\/    29700000000            8820900000000000000                               _____________________________________________________|
    |                    /                 ___________________________________                                                                   |                                                                                       /                 ___________________________________ || |                    /                 ___________________________________                                                                   |                                                                                     /                 ___________________________________ || |                                                                              /                 ___________________________________ |
    |                   /    40184897    \/ 142442181927182540809472643836930                                                                    |                                                                                      /    40184897    \/ 142442181927182540809472643836930  || |                   /    40184897    \/ 142442181927182540809472643836930                                                                    |                                                                                    /    40184897    \/ 142442181927182540809472643836930  || |                                                                             /    40184897    \/ 142442181927182540809472643836930  |
    |  1782000000000*3 /   ----------- + -------------------------------------                                                                   |                                                                     1782000000000*3 /   ----------- + ------------------------------------- || |  1782000000000*3 /   ----------- + -------------------------------------                                                                   |                                                                   1782000000000*3 /   ----------- + ------------------------------------- || |                                                             891000000000*3 /   ----------- + ------------------------------------- |
    \                \/    29700000000            8820900000000000000                                                                            \                                                                                   \/    29700000000            8820900000000000000          // \                \/    29700000000            8820900000000000000                                                                            \                                                                                 \/    29700000000            8820900000000000000          // \                                                                          \/    29700000000            8820900000000000000          /
    $$\left(- \frac{\sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} - \frac{5933033}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + i \left(- \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} - \frac{5933033}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}{2} + \frac{5933033 \sqrt{3}}{1782000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}}\right)\right) \left(\frac{5933033}{891000000000 \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}} + \sqrt[3]{\frac{\sqrt{142442181927182540809472643836930}}{8820900000000000000} + \frac{40184897}{29700000000}}\right)$$
    =
      40184897 
    -----------
    14850000000
    $$\frac{40184897}{14850000000}$$
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