Решение уравнений/ Любые/ x^4=x+4

x^4=x+4 (уравнение)

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    Найду корень уравнения: x^4=x+4

    Решение

    Вы ввели [src]
     4        
x  = x + 4
    $$x^{4} = x + 4$$
    График
    Быстрый ответ [src]
                                                                                                                                                                                                                      /   /          ________________                                                                                           \\                                                                                                                                              /   /          ________________                                                                                           \\
                                                                                                                                                                                                                  |   |         /        _______                                                                                            ||                                                                                                                                              |   |         /        _______                                                                                            ||
                                                                                                                                                                                                                  |   |        /  1    \/ 49233                                   2                                            8            ||                                                                                                                                              |   |        /  1    \/ 49233                                   2                                            8            ||
                                                                                                                                                                                                                  |   | - 2*3 /   -- + ---------  - ------------------------------------------------------------- + ----------------------- ||                                                                                                                                              |   | - 2*3 /   -- + ---------  - ------------------------------------------------------------- + ----------------------- ||
                                                                                                                                                                                                                  |   |     \/    16      144                 ___________________________________________________          ________________ ||                                                                                                                                              |   |     \/    16      144                 ___________________________________________________          ________________ ||
                                                                                                                                                                                                                  |   |                                      /        ________________                                    /        _______  ||                                                                                                                                              |   |                                      /        ________________                                    /        _______  ||
                                                                                                                                                                                                                  |   |                                     /        /        _______                                    /  1    \/ 49233   ||                                                                                                                                              |   |                                     /        /        _______                                    /  1    \/ 49233   ||
                                                                                                                                                                                                                  |   |                                    /        /  1    \/ 49233                8               3*3 /   -- + ---------  ||                                                                                                                                              |   |                                    /        /  1    \/ 49233                8               3*3 /   -- + ---------  ||
                                                                                                                                                                                                                  |   |                                   /    2*3 /   -- + ---------  - -----------------------      \/    16      144     ||                                                                                                                                              |   |                                   /    2*3 /   -- + ---------  - -----------------------      \/    16      144     ||
                                                                                                                                                                                                                  |   |                                  /       \/    16      144              ________________                            ||                                                                                                                                              |   |                                  /       \/    16      144              ________________                            ||
                                                                                                                                                                                                                  |   |                                 /                                      /        _______                             ||                                                                                                                                              |   |                                 /                                      /        _______                             ||
                                                                                                                                                                                                                  |   |                                /                                      /  1    \/ 49233                              ||                                                                                                                                              |   |                                /                                      /  1    \/ 49233                              ||
                                                                                                                                                                                                                  |   |                               /                                  3*3 /   -- + ---------                             ||                                                                                                                                              |   |                               /                                  3*3 /   -- + ---------                             ||
                                                                                                                                                                                                                  |   |                             \/                                     \/    16      144                                ||                                                                                                                                              |   |                             \/                                     \/    16      144                                ||
                                                                                                                                                                                                                  |log|---------------------------------------------------------------------------------------------------------------------||                                                                                                                                              |log|---------------------------------------------------------------------------------------------------------------------||
                                                                                                                                                                                                                  |   ||         ________________                                                                                          |||                                                                                                                                              |   ||         ________________                                                                                          |||
                                                                                                                                                                                                                  |   ||        /        _______                                                                                           |||                                                                                                                                              |   ||        /        _______                                                                                           |||
                                                                                                                                                                                                                  |   ||       /  1    \/ 49233                                   2                                            8           |||                                                                                                                                              |   ||       /  1    \/ 49233                                   2                                            8           |||
                                                                                                                                                                                                                  |   ||- 2*3 /   -- + ---------  - ------------------------------------------------------------- + -----------------------|||                                                                                                                                              |   ||- 2*3 /   -- + ---------  - ------------------------------------------------------------- + -----------------------|||
                                                                                                                                                                                                                  |   ||    \/    16      144                 ___________________________________________________          ________________|||                                                                                                                                              |   ||    \/    16      144                 ___________________________________________________          ________________|||
                                                                                                                                                                                                                  |   ||                                     /        ________________                                    /        _______ |||                                                                                                                                              |   ||                                     /        ________________                                    /        _______ |||
                                                                                                                                                                                                                  |   ||                                    /        /        _______                                    /  1    \/ 49233  |||                                                                                                                                              |   ||                                    /        /        _______                                    /  1    \/ 49233  |||
                                                                                                                                                                                                                  |   ||                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |||                                                                                                                                              |   ||                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |||
                                                                                                                                                                                                                  |   ||                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |||                                                                                                                                              |   ||                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |||
                                                                                                                                                                                                                  |   ||                                 /       \/    16      144              ________________                           |||                                                                                                                                              |   ||                                 /       \/    16      144              ________________                           |||
                                                                                      _______________________________________________________________________________________________________________________     |   ||                                /                                      /        _______                            |||                  _______________________________________________________________________________________________________________________     |   ||                                /                                      /        _______                            |||
                                                                                     / |         ________________                                                                                          |      |   ||                               /                                      /  1    \/ 49233                             |||                 / |         ________________                                                                                          |      |   ||                               /                                      /  1    \/ 49233                             |||
                                                                                    /  |        /        _______                                                                                           |      |   ||                              /                                  3*3 /   -- + ---------                            |||                /  |        /        _______                                                                                           |      |   ||                              /                                  3*3 /   -- + ---------                            |||
                                                                                   /   |       /  1    \/ 49233                                   2                                            8           |      |   \|                            \/                                     \/    16      144                               |/|               /   |       /  1    \/ 49233                                   2                                            8           |      |   \|                            \/                                     \/    16      144                               |/|
                                                                                  /    |- 2*3 /   -- + ---------  - ------------------------------------------------------------- + -----------------------| *cosh|--------------------------------------------------------------------------------------------------------------------------|              /    |- 2*3 /   -- + ---------  - ------------------------------------------------------------- + -----------------------| *sinh|--------------------------------------------------------------------------------------------------------------------------|
                 ___________________________________________________             /     |    \/    16      144                 ___________________________________________________          ________________|      \                                                            2                                                             /             /     |    \/    16      144                 ___________________________________________________          ________________|      \                                                            2                                                             /
                /        ________________                                       /      |                                     /        ________________                                    /        _______ |                                                                                                                                              /      |                                     /        ________________                                    /        _______ |                                                                                                                                  
               /        /        _______                                       /       |                                    /        /        _______                                    /  1    \/ 49233  |                                                                                                                                             /       |                                    /        /        _______                                    /  1    \/ 49233  |                                                                                                                                  
              /        /  1    \/ 49233                8                      /        |                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |                                                                                                                                            /        |                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |                                                                                                                                  
             /    2*3 /   -- + ---------  - -----------------------          /         |                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |                                                                                                                                           /         |                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |                                                                                                                                  
            /       \/    16      144              ________________         /          |                                 /       \/    16      144              ________________                           |                                                                                                                                          /          |                                 /       \/    16      144              ________________                           |                                                                                                                                  
           /                                      /        _______         /           |                                /                                      /        _______                            |                                                                                                                                         /           |                                /                                      /        _______                            |                                                                                                                                  
          /                                      /  1    \/ 49233         /            |                               /                                      /  1    \/ 49233                             |                                                                                                                                        /            |                               /                                      /  1    \/ 49233                             |                                                                                                                                  
         /                                  3*3 /   -- + ---------       /             |                              /                                  3*3 /   -- + ---------                            |                                                                                                                                       /             |                              /                                  3*3 /   -- + ---------                            |                                                                                                                                  
       \/                                     \/    16      144        \/              |                            \/                                     \/    16      144                               |                                                                                                                                     \/              |                            \/                                     \/    16      144                               |                                                                                                                                  
x1 = - ------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                     2                                                                                                                                                                    2                                                                                                                                                                                                                                                                         2
    $$x_{1} = - \frac{1}{2} \sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} - \frac{1}{2} \cosh{\left (\frac{1}{2} \log{\left (\frac{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}{\left|{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}\right|} \right )} \right )} \sqrt{\left|{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}\right|} - \frac{1}{2} \sinh{\left (\frac{1}{2} \log{\left (\frac{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}{\left|{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}\right|} \right )} \right )} \sqrt{\left|{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}\right|}$$
                                                                                                                                                                                                                      /   /          ________________                                                                                           \\                                                                                                                                              /   /          ________________                                                                                           \\
                                                                                                                                                                                                                  |   |         /        _______                                                                                            ||                                                                                                                                              |   |         /        _______                                                                                            ||
                                                                                                                                                                                                                  |   |        /  1    \/ 49233                                   2                                            8            ||                                                                                                                                              |   |        /  1    \/ 49233                                   2                                            8            ||
                                                                                                                                                                                                                  |   | - 2*3 /   -- + ---------  - ------------------------------------------------------------- + ----------------------- ||                                                                                                                                              |   | - 2*3 /   -- + ---------  - ------------------------------------------------------------- + ----------------------- ||
                                                                                                                                                                                                                  |   |     \/    16      144                 ___________________________________________________          ________________ ||                                                                                                                                              |   |     \/    16      144                 ___________________________________________________          ________________ ||
                                                                                                                                                                                                                  |   |                                      /        ________________                                    /        _______  ||                                                                                                                                              |   |                                      /        ________________                                    /        _______  ||
                                                                                                                                                                                                                  |   |                                     /        /        _______                                    /  1    \/ 49233   ||                                                                                                                                              |   |                                     /        /        _______                                    /  1    \/ 49233   ||
                                                                                                                                                                                                                  |   |                                    /        /  1    \/ 49233                8               3*3 /   -- + ---------  ||                                                                                                                                              |   |                                    /        /  1    \/ 49233                8               3*3 /   -- + ---------  ||
                                                                                                                                                                                                                  |   |                                   /    2*3 /   -- + ---------  - -----------------------      \/    16      144     ||                                                                                                                                              |   |                                   /    2*3 /   -- + ---------  - -----------------------      \/    16      144     ||
                                                                                                                                                                                                                  |   |                                  /       \/    16      144              ________________                            ||                                                                                                                                              |   |                                  /       \/    16      144              ________________                            ||
                                                                                                                                                                                                                  |   |                                 /                                      /        _______                             ||                                                                                                                                              |   |                                 /                                      /        _______                             ||
                                                                                                                                                                                                                  |   |                                /                                      /  1    \/ 49233                              ||                                                                                                                                              |   |                                /                                      /  1    \/ 49233                              ||
                                                                                                                                                                                                                  |   |                               /                                  3*3 /   -- + ---------                             ||                                                                                                                                              |   |                               /                                  3*3 /   -- + ---------                             ||
                                                                                                                                                                                                                  |   |                             \/                                     \/    16      144                                ||                                                                                                                                              |   |                             \/                                     \/    16      144                                ||
                                                                                                                                                                                                                  |log|---------------------------------------------------------------------------------------------------------------------||                                                                                                                                              |log|---------------------------------------------------------------------------------------------------------------------||
                                                                                                                                                                                                                  |   ||         ________________                                                                                          |||                                                                                                                                              |   ||         ________________                                                                                          |||
                                                                                                                                                                                                                  |   ||        /        _______                                                                                           |||                                                                                                                                              |   ||        /        _______                                                                                           |||
                                                                                                                                                                                                                  |   ||       /  1    \/ 49233                                   2                                            8           |||                                                                                                                                              |   ||       /  1    \/ 49233                                   2                                            8           |||
                                                                                                                                                                                                                  |   ||- 2*3 /   -- + ---------  - ------------------------------------------------------------- + -----------------------|||                                                                                                                                              |   ||- 2*3 /   -- + ---------  - ------------------------------------------------------------- + -----------------------|||
                                                                                                                                                                                                                  |   ||    \/    16      144                 ___________________________________________________          ________________|||                                                                                                                                              |   ||    \/    16      144                 ___________________________________________________          ________________|||
                                                                                                                                                                                                                  |   ||                                     /        ________________                                    /        _______ |||                                                                                                                                              |   ||                                     /        ________________                                    /        _______ |||
                                                                                                                                                                                                                  |   ||                                    /        /        _______                                    /  1    \/ 49233  |||                                                                                                                                              |   ||                                    /        /        _______                                    /  1    \/ 49233  |||
                                                                                                                                                                                                                  |   ||                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |||                                                                                                                                              |   ||                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |||
                                                                                                                                                                                                                  |   ||                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |||                                                                                                                                              |   ||                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |||
                                                                                                                                                                                                                  |   ||                                 /       \/    16      144              ________________                           |||                                                                                                                                              |   ||                                 /       \/    16      144              ________________                           |||
                                                                                      _______________________________________________________________________________________________________________________     |   ||                                /                                      /        _______                            |||                  _______________________________________________________________________________________________________________________     |   ||                                /                                      /        _______                            |||
                                                                                     / |         ________________                                                                                          |      |   ||                               /                                      /  1    \/ 49233                             |||                 / |         ________________                                                                                          |      |   ||                               /                                      /  1    \/ 49233                             |||
                                                                                    /  |        /        _______                                                                                           |      |   ||                              /                                  3*3 /   -- + ---------                            |||                /  |        /        _______                                                                                           |      |   ||                              /                                  3*3 /   -- + ---------                            |||
                                                                                   /   |       /  1    \/ 49233                                   2                                            8           |      |   \|                            \/                                     \/    16      144                               |/|               /   |       /  1    \/ 49233                                   2                                            8           |      |   \|                            \/                                     \/    16      144                               |/|
                                                                                  /    |- 2*3 /   -- + ---------  - ------------------------------------------------------------- + -----------------------| *cosh|--------------------------------------------------------------------------------------------------------------------------|              /    |- 2*3 /   -- + ---------  - ------------------------------------------------------------- + -----------------------| *sinh|--------------------------------------------------------------------------------------------------------------------------|
                 ___________________________________________________             /     |    \/    16      144                 ___________________________________________________          ________________|      \                                                            2                                                             /             /     |    \/    16      144                 ___________________________________________________          ________________|      \                                                            2                                                             /
                /        ________________                                       /      |                                     /        ________________                                    /        _______ |                                                                                                                                              /      |                                     /        ________________                                    /        _______ |                                                                                                                                  
               /        /        _______                                       /       |                                    /        /        _______                                    /  1    \/ 49233  |                                                                                                                                             /       |                                    /        /        _______                                    /  1    \/ 49233  |                                                                                                                                  
              /        /  1    \/ 49233                8                      /        |                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |                                                                                                                                            /        |                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |                                                                                                                                  
             /    2*3 /   -- + ---------  - -----------------------          /         |                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |                                                                                                                                           /         |                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |                                                                                                                                  
            /       \/    16      144              ________________         /          |                                 /       \/    16      144              ________________                           |                                                                                                                                          /          |                                 /       \/    16      144              ________________                           |                                                                                                                                  
           /                                      /        _______         /           |                                /                                      /        _______                            |                                                                                                                                         /           |                                /                                      /        _______                            |                                                                                                                                  
          /                                      /  1    \/ 49233         /            |                               /                                      /  1    \/ 49233                             |                                                                                                                                        /            |                               /                                      /  1    \/ 49233                             |                                                                                                                                  
         /                                  3*3 /   -- + ---------       /             |                              /                                  3*3 /   -- + ---------                            |                                                                                                                                       /             |                              /                                  3*3 /   -- + ---------                            |                                                                                                                                  
       \/                                     \/    16      144        \/              |                            \/                                     \/    16      144                               |                                                                                                                                     \/              |                            \/                                     \/    16      144                               |                                                                                                                                  
x2 = - ------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                     2                                                                                                                                                                    2                                                                                                                                                                                                                                                                         2
    $$x_{2} = - \frac{1}{2} \sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{1}{2} \cosh{\left (\frac{1}{2} \log{\left (\frac{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}{\left|{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}\right|} \right )} \right )} \sqrt{\left|{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}\right|} + \frac{1}{2} \sinh{\left (\frac{1}{2} \log{\left (\frac{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}{\left|{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}\right|} \right )} \right )} \sqrt{\left|{- \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}} - 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}\right|}$$
                                                                                                                                                                                                                    /   /          ________________                                                                                           \\                                                                                                                                              /   /          ________________                                                                                           \\
                                                                                                                                                                                                                |   |         /        _______                                                                                            ||                                                                                                                                              |   |         /        _______                                                                                            ||
                                                                                                                                                                                                                |   |        /  1    \/ 49233                                   2                                            8            ||                                                                                                                                              |   |        /  1    \/ 49233                                   2                                            8            ||
                                                                                                                                                                                                                |   | - 2*3 /   -- + ---------  + ------------------------------------------------------------- + ----------------------- ||                                                                                                                                              |   | - 2*3 /   -- + ---------  + ------------------------------------------------------------- + ----------------------- ||
                                                                                                                                                                                                                |   |     \/    16      144                 ___________________________________________________          ________________ ||                                                                                                                                              |   |     \/    16      144                 ___________________________________________________          ________________ ||
                                                                                                                                                                                                                |   |                                      /        ________________                                    /        _______  ||                                                                                                                                              |   |                                      /        ________________                                    /        _______  ||
                                                                                                                                                                                                                |   |                                     /        /        _______                                    /  1    \/ 49233   ||                                                                                                                                              |   |                                     /        /        _______                                    /  1    \/ 49233   ||
                                                                                                                                                                                                                |   |                                    /        /  1    \/ 49233                8               3*3 /   -- + ---------  ||                                                                                                                                              |   |                                    /        /  1    \/ 49233                8               3*3 /   -- + ---------  ||
                                                                                                                                                                                                                |   |                                   /    2*3 /   -- + ---------  - -----------------------      \/    16      144     ||                                                                                                                                              |   |                                   /    2*3 /   -- + ---------  - -----------------------      \/    16      144     ||
                                                                                                                                                                                                                |   |                                  /       \/    16      144              ________________                            ||                                                                                                                                              |   |                                  /       \/    16      144              ________________                            ||
                                                                                                                                                                                                                |   |                                 /                                      /        _______                             ||                                                                                                                                              |   |                                 /                                      /        _______                             ||
                                                                                                                                                                                                                |   |                                /                                      /  1    \/ 49233                              ||                                                                                                                                              |   |                                /                                      /  1    \/ 49233                              ||
                                                                                                                                                                                                                |   |                               /                                  3*3 /   -- + ---------                             ||                                                                                                                                              |   |                               /                                  3*3 /   -- + ---------                             ||
                                                                                                                                                                                                                |   |                             \/                                     \/    16      144                                ||                                                                                                                                              |   |                             \/                                     \/    16      144                                ||
                                                                                                                                                                                                                |log|---------------------------------------------------------------------------------------------------------------------||                                                                                                                                              |log|---------------------------------------------------------------------------------------------------------------------||
                                                                                                                                                                                                                |   ||         ________________                                                                                          |||                                                                                                                                              |   ||         ________________                                                                                          |||
                                                                                                                                                                                                                |   ||        /        _______                                                                                           |||                                                                                                                                              |   ||        /        _______                                                                                           |||
                                                                                                                                                                                                                |   ||       /  1    \/ 49233                                   2                                            8           |||                                                                                                                                              |   ||       /  1    \/ 49233                                   2                                            8           |||
                                                                                                                                                                                                                |   ||- 2*3 /   -- + ---------  + ------------------------------------------------------------- + -----------------------|||                                                                                                                                              |   ||- 2*3 /   -- + ---------  + ------------------------------------------------------------- + -----------------------|||
                                                                                                                                                                                                                |   ||    \/    16      144                 ___________________________________________________          ________________|||                                                                                                                                              |   ||    \/    16      144                 ___________________________________________________          ________________|||
                                                                                                                                                                                                                |   ||                                     /        ________________                                    /        _______ |||                                                                                                                                              |   ||                                     /        ________________                                    /        _______ |||
                                                                                                                                                                                                                |   ||                                    /        /        _______                                    /  1    \/ 49233  |||                                                                                                                                              |   ||                                    /        /        _______                                    /  1    \/ 49233  |||
                                                                                                                                                                                                                |   ||                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |||                                                                                                                                              |   ||                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |||
                                                                                                                                                                                                                |   ||                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |||                                                                                                                                              |   ||                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |||
                                                                                                                                                                                                                |   ||                                 /       \/    16      144              ________________                           |||                                                                                                                                              |   ||                                 /       \/    16      144              ________________                           |||
                                                                                    _______________________________________________________________________________________________________________________     |   ||                                /                                      /        _______                            |||                  _______________________________________________________________________________________________________________________     |   ||                                /                                      /        _______                            |||
                                                                                   / |         ________________                                                                                          |      |   ||                               /                                      /  1    \/ 49233                             |||                 / |         ________________                                                                                          |      |   ||                               /                                      /  1    \/ 49233                             |||
                                                                                  /  |        /        _______                                                                                           |      |   ||                              /                                  3*3 /   -- + ---------                            |||                /  |        /        _______                                                                                           |      |   ||                              /                                  3*3 /   -- + ---------                            |||
                                                                                 /   |       /  1    \/ 49233                                   2                                            8           |      |   \|                            \/                                     \/    16      144                               |/|               /   |       /  1    \/ 49233                                   2                                            8           |      |   \|                            \/                                     \/    16      144                               |/|
                                                                                /    |- 2*3 /   -- + ---------  + ------------------------------------------------------------- + -----------------------| *cosh|--------------------------------------------------------------------------------------------------------------------------|              /    |- 2*3 /   -- + ---------  + ------------------------------------------------------------- + -----------------------| *sinh|--------------------------------------------------------------------------------------------------------------------------|
               ___________________________________________________             /     |    \/    16      144                 ___________________________________________________          ________________|      \                                                            2                                                             /             /     |    \/    16      144                 ___________________________________________________          ________________|      \                                                            2                                                             /
              /        ________________                                       /      |                                     /        ________________                                    /        _______ |                                                                                                                                              /      |                                     /        ________________                                    /        _______ |                                                                                                                                  
             /        /        _______                                       /       |                                    /        /        _______                                    /  1    \/ 49233  |                                                                                                                                             /       |                                    /        /        _______                                    /  1    \/ 49233  |                                                                                                                                  
            /        /  1    \/ 49233                8                      /        |                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |                                                                                                                                            /        |                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |                                                                                                                                  
           /    2*3 /   -- + ---------  - -----------------------          /         |                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |                                                                                                                                           /         |                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |                                                                                                                                  
          /       \/    16      144              ________________         /          |                                 /       \/    16      144              ________________                           |                                                                                                                                          /          |                                 /       \/    16      144              ________________                           |                                                                                                                                  
         /                                      /        _______         /           |                                /                                      /        _______                            |                                                                                                                                         /           |                                /                                      /        _______                            |                                                                                                                                  
        /                                      /  1    \/ 49233         /            |                               /                                      /  1    \/ 49233                             |                                                                                                                                        /            |                               /                                      /  1    \/ 49233                             |                                                                                                                                  
       /                                  3*3 /   -- + ---------       /             |                              /                                  3*3 /   -- + ---------                            |                                                                                                                                       /             |                              /                                  3*3 /   -- + ---------                            |                                                                                                                                  
     \/                                     \/    16      144        \/              |                            \/                                     \/    16      144                               |                                                                                                                                     \/              |                            \/                                     \/    16      144                               |                                                                                                                                  
x3 = ------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                   2                                                                                                                                                                    2                                                                                                                                                                                                                                                                         2
    $$x_{3} = \frac{1}{2} \sinh{\left (\frac{1}{2} \log{\left (\frac{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}{\left|{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}\right|} \right )} \right )} \sqrt{\left|{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}\right|} + \frac{1}{2} \sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{1}{2} \cosh{\left (\frac{1}{2} \log{\left (\frac{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}{\left|{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}\right|} \right )} \right )} \sqrt{\left|{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}\right|}$$
                                                                                                                                                                                                                    /   /          ________________                                                                                           \\                                                                                                                                              /   /          ________________                                                                                           \\
                                                                                                                                                                                                                |   |         /        _______                                                                                            ||                                                                                                                                              |   |         /        _______                                                                                            ||
                                                                                                                                                                                                                |   |        /  1    \/ 49233                                   2                                            8            ||                                                                                                                                              |   |        /  1    \/ 49233                                   2                                            8            ||
                                                                                                                                                                                                                |   | - 2*3 /   -- + ---------  + ------------------------------------------------------------- + ----------------------- ||                                                                                                                                              |   | - 2*3 /   -- + ---------  + ------------------------------------------------------------- + ----------------------- ||
                                                                                                                                                                                                                |   |     \/    16      144                 ___________________________________________________          ________________ ||                                                                                                                                              |   |     \/    16      144                 ___________________________________________________          ________________ ||
                                                                                                                                                                                                                |   |                                      /        ________________                                    /        _______  ||                                                                                                                                              |   |                                      /        ________________                                    /        _______  ||
                                                                                                                                                                                                                |   |                                     /        /        _______                                    /  1    \/ 49233   ||                                                                                                                                              |   |                                     /        /        _______                                    /  1    \/ 49233   ||
                                                                                                                                                                                                                |   |                                    /        /  1    \/ 49233                8               3*3 /   -- + ---------  ||                                                                                                                                              |   |                                    /        /  1    \/ 49233                8               3*3 /   -- + ---------  ||
                                                                                                                                                                                                                |   |                                   /    2*3 /   -- + ---------  - -----------------------      \/    16      144     ||                                                                                                                                              |   |                                   /    2*3 /   -- + ---------  - -----------------------      \/    16      144     ||
                                                                                                                                                                                                                |   |                                  /       \/    16      144              ________________                            ||                                                                                                                                              |   |                                  /       \/    16      144              ________________                            ||
                                                                                                                                                                                                                |   |                                 /                                      /        _______                             ||                                                                                                                                              |   |                                 /                                      /        _______                             ||
                                                                                                                                                                                                                |   |                                /                                      /  1    \/ 49233                              ||                                                                                                                                              |   |                                /                                      /  1    \/ 49233                              ||
                                                                                                                                                                                                                |   |                               /                                  3*3 /   -- + ---------                             ||                                                                                                                                              |   |                               /                                  3*3 /   -- + ---------                             ||
                                                                                                                                                                                                                |   |                             \/                                     \/    16      144                                ||                                                                                                                                              |   |                             \/                                     \/    16      144                                ||
                                                                                                                                                                                                                |log|---------------------------------------------------------------------------------------------------------------------||                                                                                                                                              |log|---------------------------------------------------------------------------------------------------------------------||
                                                                                                                                                                                                                |   ||         ________________                                                                                          |||                                                                                                                                              |   ||         ________________                                                                                          |||
                                                                                                                                                                                                                |   ||        /        _______                                                                                           |||                                                                                                                                              |   ||        /        _______                                                                                           |||
                                                                                                                                                                                                                |   ||       /  1    \/ 49233                                   2                                            8           |||                                                                                                                                              |   ||       /  1    \/ 49233                                   2                                            8           |||
                                                                                                                                                                                                                |   ||- 2*3 /   -- + ---------  + ------------------------------------------------------------- + -----------------------|||                                                                                                                                              |   ||- 2*3 /   -- + ---------  + ------------------------------------------------------------- + -----------------------|||
                                                                                                                                                                                                                |   ||    \/    16      144                 ___________________________________________________          ________________|||                                                                                                                                              |   ||    \/    16      144                 ___________________________________________________          ________________|||
                                                                                                                                                                                                                |   ||                                     /        ________________                                    /        _______ |||                                                                                                                                              |   ||                                     /        ________________                                    /        _______ |||
                                                                                                                                                                                                                |   ||                                    /        /        _______                                    /  1    \/ 49233  |||                                                                                                                                              |   ||                                    /        /        _______                                    /  1    \/ 49233  |||
                                                                                                                                                                                                                |   ||                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |||                                                                                                                                              |   ||                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |||
                                                                                                                                                                                                                |   ||                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |||                                                                                                                                              |   ||                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |||
                                                                                                                                                                                                                |   ||                                 /       \/    16      144              ________________                           |||                                                                                                                                              |   ||                                 /       \/    16      144              ________________                           |||
                                                                                    _______________________________________________________________________________________________________________________     |   ||                                /                                      /        _______                            |||                  _______________________________________________________________________________________________________________________     |   ||                                /                                      /        _______                            |||
                                                                                   / |         ________________                                                                                          |      |   ||                               /                                      /  1    \/ 49233                             |||                 / |         ________________                                                                                          |      |   ||                               /                                      /  1    \/ 49233                             |||
                                                                                  /  |        /        _______                                                                                           |      |   ||                              /                                  3*3 /   -- + ---------                            |||                /  |        /        _______                                                                                           |      |   ||                              /                                  3*3 /   -- + ---------                            |||
                                                                                 /   |       /  1    \/ 49233                                   2                                            8           |      |   \|                            \/                                     \/    16      144                               |/|               /   |       /  1    \/ 49233                                   2                                            8           |      |   \|                            \/                                     \/    16      144                               |/|
                                                                                /    |- 2*3 /   -- + ---------  + ------------------------------------------------------------- + -----------------------| *cosh|--------------------------------------------------------------------------------------------------------------------------|              /    |- 2*3 /   -- + ---------  + ------------------------------------------------------------- + -----------------------| *sinh|--------------------------------------------------------------------------------------------------------------------------|
               ___________________________________________________             /     |    \/    16      144                 ___________________________________________________          ________________|      \                                                            2                                                             /             /     |    \/    16      144                 ___________________________________________________          ________________|      \                                                            2                                                             /
              /        ________________                                       /      |                                     /        ________________                                    /        _______ |                                                                                                                                              /      |                                     /        ________________                                    /        _______ |                                                                                                                                  
             /        /        _______                                       /       |                                    /        /        _______                                    /  1    \/ 49233  |                                                                                                                                             /       |                                    /        /        _______                                    /  1    \/ 49233  |                                                                                                                                  
            /        /  1    \/ 49233                8                      /        |                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |                                                                                                                                            /        |                                   /        /  1    \/ 49233                8               3*3 /   -- + --------- |                                                                                                                                  
           /    2*3 /   -- + ---------  - -----------------------          /         |                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |                                                                                                                                           /         |                                  /    2*3 /   -- + ---------  - -----------------------      \/    16      144    |                                                                                                                                  
          /       \/    16      144              ________________         /          |                                 /       \/    16      144              ________________                           |                                                                                                                                          /          |                                 /       \/    16      144              ________________                           |                                                                                                                                  
         /                                      /        _______         /           |                                /                                      /        _______                            |                                                                                                                                         /           |                                /                                      /        _______                            |                                                                                                                                  
        /                                      /  1    \/ 49233         /            |                               /                                      /  1    \/ 49233                             |                                                                                                                                        /            |                               /                                      /  1    \/ 49233                             |                                                                                                                                  
       /                                  3*3 /   -- + ---------       /             |                              /                                  3*3 /   -- + ---------                            |                                                                                                                                       /             |                              /                                  3*3 /   -- + ---------                            |                                                                                                                                  
     \/                                     \/    16      144        \/              |                            \/                                     \/    16      144                               |                                                                                                                                     \/              |                            \/                                     \/    16      144                               |                                                                                                                                  
x4 = ------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                   2                                                                                                                                                                    2                                                                                                                                                                                                                                                                         2
    $$x_{4} = - \frac{1}{2} \cosh{\left (\frac{1}{2} \log{\left (\frac{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}{\left|{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}\right|} \right )} \right )} \sqrt{\left|{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}\right|} - \frac{1}{2} \sinh{\left (\frac{1}{2} \log{\left (\frac{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}{\left|{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}\right|} \right )} \right )} \sqrt{\left|{- 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}} + \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + \frac{2}{\sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}}}\right|} + \frac{1}{2} \sqrt{- \frac{8}{3 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}} + 2 \sqrt[3]{\frac{1}{16} + \frac{\sqrt{49233}}{144}}}$$
    Численный ответ [src]
    x1 = -0.124984751446 - 1.4198116758*i
    x2 = -1.28378166586000
    x3 = -0.124984751446 + 1.4198116758*i
    x4 = 1.53375116876000
    График
    x^4=x+4 (уравнение) /media/krcore-image-pods/a28f/9d4f/b222/b855/im.png