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x^4-4*(x^3)*y+2*(x^2)*(y^2)-4*x*(y^3)+y^4-0,8y=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
 4      3        2  2        3    4   4*y    
x  - 4*x *y + 2*x *y  - 4*x*y  + y  - --- = 0
                                       5     
$$- \frac{4 y}{5} + \left(y^{4} + \left(- 4 x y^{3} + \left(2 x^{2} y^{2} + \left(x^{4} - 4 x^{3} y\right)\right)\right)\right) = 0$$
Gráfica
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         ||                                                                                                                                                                                                                                                                                        y - ---------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------                                                                                                                                                                                                                                                                                          for --- + ---- = 0|     ||                                                                                                                                                                                                                                                                                        y - ---------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------                                                                                                                                                                                                                                                                                          for --- + ---- = 0|
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x1 = I*im|<                                                                                                                                                                                                                                                                               /               /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    16*y                                                                                                                          16*y                                                                                                                                                                           \ 5     3  /                                                                  | + re|<                                                                                                                                                                                                                                                                               /               /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    16*y                                                                                                                          16*y                                                                                                                                                                           \ 5     3  /                                                                  |
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         ||               /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------               /                                                                                                                                                    /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------      \/         \/                        4                         27           27              3                               |     ||               /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------               /                                                                                                                                                    /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------      \/         \/                        4                         27           27              3                               |
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         ||      /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------       /                                                                                                                                                    /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                                                                                                                                   |     ||      /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------       /                                                                                                                                                    /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                                                                                                                                   |
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$$x_{1} = \operatorname{re}{\left(\begin{cases} y - \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} - \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y - \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} y - \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} - \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y - \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
         //                                                                                                                                                                                                                                                                                                         _______________________________________________________________________________________________________________                                                                                                                                                                                                                                                                                                                                                                         \     //                                                                                                                                                                                                                                                                                                         _______________________________________________________________________________________________________________                                                                                                                                                                                                                                                                                                                                                                         \
         ||                                                                                                                                                                                                                                                                                                        /         ________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                               |     ||                                                                                                                                                                                                                                                                                                        /         ________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                               |
         ||                                                                                                                                                                                                                                                                                                       /         /               2 /     4   4*y\                                                                                                                                                                                                                                                                                                                                                                                                                                                |     ||                                                                                                                                                                                                                                                                                                       /         /               2 /     4   4*y\                                                                                                                                                                                                                                                                                                                                                                                                                                                |
         ||                                                                                                                                                                                                                                                                                                      /         /         6   4*y *|- 4*y  - ---|        2                                 3                                                                                                                                                                                                                                                                                                                                                                                                     |     ||                                                                                                                                                                                                                                                                                                      /         /         6   4*y *|- 4*y  - ---|        2                                 3                                                                                                                                                                                                                                                                                                                                                                                                     |
         ||                                                                                                                                                                                                                                                                                                     /         /     200*y         \          5 /    16*y                              16*y                                                                                                                                                                                                                                                                                                                                                                                                      |     ||                                                                                                                                                                                                                                                                                                     /         /     200*y         \          5 /    16*y                              16*y                                                                                                                                                                                                                                                                                                                                                                                                      |
         ||                                                                                                                                                                                                                                                                                                    /     2*3 /    - ------ - -------------------  + ----- - ----------------------------------------------------------                                                                                                                                                                                                                                                                                                                                                                          |     ||                                                                                                                                                                                                                                                                                                    /     2*3 /    - ------ - -------------------  + ----- - ----------------------------------------------------------                                                                                                                                                                                                                                                                                                                                                                          |
         ||                                                                                                                                                                                                                                                                                                   /        \/         27              3               3            ___________________________________________________           ___________________________________________________                                                                                                                                                                                                                                                                                                            |     ||                                                                                                                                                                                                                                                                                                   /        \/         27              3               3            ___________________________________________________           ___________________________________________________                                                                                                                                                                                                                                                                                                            |
         ||                                                                                                                                                                                                                                                                                                  /                                                                /           ________________________________                  /           ________________________________                                                                                                                                                                                                                                                                                                                    |     ||                                                                                                                                                                                                                                                                                                  /                                                                /           ________________________________                  /           ________________________________                                                                                                                                                                                                                                                                                                                    |
         ||                                                                                                                                                                                                                                                                                                 /                                                                /           /               2 /     4   4*y\                  /           /               2 /     4   4*y\                                                                                                                                                                                                                                                                                                                     |     ||                                                                                                                                                                                                                                                                                                 /                                                                /           /               2 /     4   4*y\                  /           /               2 /     4   4*y\                                                                                                                                                                                                                                                                                                                     |
         ||                                                                                                                                                                                                                                                                                                /                                                                /           /         6   4*y *|- 4*y  - ---|       2         /           /         6   4*y *|- 4*y  - ---|       2                                                                                                                                                                                                                                                                                                             |     ||                                                                                                                                                                                                                                                                                                /                                                                /           /         6   4*y *|- 4*y  - ---|       2         /           /         6   4*y *|- 4*y  - ---|       2                                                                                                                                                                                                                                                                                                             |
         ||                                                                                                                                                                                                                                                                                               /                                                                /           /     200*y         \          5 /    8*y         /           /     200*y         \          5 /    8*y                                                                                                                                                                                                                                                                                                              |     ||                                                                                                                                                                                                                                                                                               /                                                                /           /     200*y         \          5 /    8*y         /           /     200*y         \          5 /    8*y                                                                                                                                                                                                                                                                                                              |
         ||                                                                                                                                                                                                                                                                                              /                                                                /     - 2*3 /    - ------ - -------------------  + ----       /     - 2*3 /    - ------ - -------------------  + ----                                                                                                                                                                                                                                                                                                        4    |     ||                                                                                                                                                                                                                                                                                              /                                                                /     - 2*3 /    - ------ - -------------------  + ----       /     - 2*3 /    - ------ - -------------------  + ----                                                                                                                                                                                                                                                                                                        4    |
         ||                                                                                                                                                                                                                                                                                            \/                                                               \/          \/         27              3              3       \/          \/         27              3              3                                                                                                                                                                                                                                                                                                 4*y   8*y     |     ||                                                                                                                                                                                                                                                                                            \/                                                               \/          \/         27              3              3       \/          \/         27              3              3                                                                                                                                                                                                                                                                                                 4*y   8*y     |
         ||                                                                                                                                                                                                                                                                                        y + ---------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------                                                                                                                                                                                                                                                                                          for --- + ---- = 0|     ||                                                                                                                                                                                                                                                                                        y + ---------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------                                                                                                                                                                                                                                                                                          for --- + ---- = 0|
         ||                                                                                                                                                                                                                                                                                                                                                         2                                                                                             2                                                                                                                                                                                                                                                                                                                            5     3      |     ||                                                                                                                                                                                                                                                                                                                                                         2                                                                                             2                                                                                                                                                                                                                                                                                                                            5     3      |
         ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |     ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
         ||                                  ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                                                                                         |     ||                                  ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________                                                                                                                                                                                                                                                                         |
         ||                                 /               _____________________________________________________________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |     ||                                 /               _____________________________________________________________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
         ||                                /               /          ___________________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |     ||                                /               /          ___________________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
         ||                               /               /          /                                 2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |     ||                               /               /          /                                 2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |
         ||                              /               /          /  /              2 /     4   4*y\\                3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |     ||                              /               /          /  /              2 /     4   4*y\\                3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |
         ||                             /               /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                                                                                                                                                                                                                                                                                  /         4\                                                                                                                                                                                                                                                                                                                       |     ||                             /               /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                                                                                                                                                                                                                                                                                  /         4\                                                                                                                                                                                                                                                                                                                       |
         ||                            /               /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                                                                                                                                                                                                                 |4*y   8*y |                                                                                                                                                                                                                                                                                                                       |     ||                            /               /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                                                                                                                                                                                                                 |4*y   8*y |                                                                                                                                                                                                                                                                                                                       |
         ||                           /               /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|        2                                                                                                                             3                                                                                                                                                                        2*|--- + ----|                                                                                                                                                                                                                                                                                                                       |     ||                           /               /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|        2                                                                                                                             3                                                                                                                                                                        2*|--- + ----|                                                                                                                                                                                                                                                                                                                       |
x2 = I*im|<                          /               /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    16*y                                                                                                                          16*y                                                                                                                                                                           \ 5     3  /                                                                                                                                                                                                                                                                                                                       | + re|<                          /               /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    16*y                                                                                                                          16*y                                                                                                                                                                           \ 5     3  /                                                                                                                                                                                                                                                                                                                       |
         ||                         /         - 2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ----- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------                                                                                                                                                                                                                                                                          |     ||                         /         - 2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ----- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------                                                                                                                                                                                                                                                                          |
         ||                        /              \/         \/                        4                         27           27              3               3                         ______________________________________________________________________________________________________________________________________________________________________________________________________________________________               _____________________________________________________________________________________________                        ______________________________________________________________________________________________________________________________________________________________________________________________________________________________                    |     ||                        /              \/         \/                        4                         27           27              3               3                         ______________________________________________________________________________________________________________________________________________________________________________________________________________________________               _____________________________________________________________________________________________                        ______________________________________________________________________________________________________________________________________________________________________________________________________________________________                    |
         ||                       /                                                                                                                                                    /             _____________________________________________________________________________________________                                                                                                                                  /          ___________________________________________________                                                       /             _____________________________________________________________________________________________                                                                                                                                        |     ||                       /                                                                                                                                                    /             _____________________________________________________________________________________________                                                                                                                                  /          ___________________________________________________                                                       /             _____________________________________________________________________________________________                                                                                                                                        |
         ||                      /                                                                                                                                                    /             /          ___________________________________________________                                                                                                                                                                 /          /                                 2                                                                       /             /          ___________________________________________________                                                                                                                                                                        |     ||                      /                                                                                                                                                    /             /          ___________________________________________________                                                                                                                                                                 /          /                                 2                                                                       /             /          ___________________________________________________                                                                                                                                                                        |
         ||                     /                                                                                                                                                    /             /          /                                 2                                                                                                                                                                                 /          /  /              2 /     4   4*y\\                3                                                      /             /          /                                 2                                                                                                                                                                                         |     ||                     /                                                                                                                                                    /             /          /                                 2                                                                                                                                                                                 /          /  /              2 /     4   4*y\\                3                                                      /             /          /                                 2                                                                                                                                                                                         |
         ||                    /                                                                                                                                                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                      /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                         |     ||                    /                                                                                                                                                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                      /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                         |
         ||                   /                                                                                                                                                    /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                        /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                    /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                                  |     ||                   /                                                                                                                                                    /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                        /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                    /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                                  |
         ||                  /                                                                                                                                                    /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                       /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                   /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                                  |     ||                  /                                                                                                                                                    /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                       /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                   /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                                  |
         ||                 /                                                                                                                                                    /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                      /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                  /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                                  |     ||                 /                                                                                                                                                    /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                      /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                  /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                                  |
         ||                /                                                                                                                                                    /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                 3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                 /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                                  |     ||                /                                                                                                                                                    /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                 3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                 /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                                  |
         ||               /                                                                                                                                                    /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------      \/         \/                        4                         27           27              3                         /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------                     |     ||               /                                                                                                                                                    /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------      \/         \/                        4                         27           27              3                         /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------                     |
         ||              /                                                                                                                                                    /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________                                                                                                                           /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________                     |     ||              /                                                                                                                                                    /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________                                                                                                                           /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________                     |
         ||             /                                                                                                                                                    /                                                                                                                                         /          ___________________________________________________                                                                                                                                                          /                                                                                                                                         /          ___________________________________________________                                                     |     ||             /                                                                                                                                                    /                                                                                                                                         /          ___________________________________________________                                                                                                                                                          /                                                                                                                                         /          ___________________________________________________                                                     |
         ||            /                                                                                                                                                    /                                                                                                                                         /          /                                 2                                                                                                                                                                          /                                                                                                                                         /          /                                 2                                                                      |     ||            /                                                                                                                                                    /                                                                                                                                         /          /                                 2                                                                                                                                                                          /                                                                                                                                         /          /                                 2                                                                      |
         ||           /                                                                                                                                                    /                                                                                                                                         /          /  /              2 /     4   4*y\\                3                                                                                                                                                         /                                                                                                                                         /          /  /              2 /     4   4*y\\                3                                                      |     ||           /                                                                                                                                                    /                                                                                                                                         /          /  /              2 /     4   4*y\\                3                                                                                                                                                         /                                                                                                                                         /          /  /              2 /     4   4*y\\                3                                                      |
         ||          /                                                                                                                                                    /                                                                                                                                         /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                                                                                         /                                                                                                                                         /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                       |     ||          /                                                                                                                                                    /                                                                                                                                         /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                                                                                         /                                                                                                                                         /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                       |
         ||         /                                                                                                                                                    /                                                                                                                                         /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                       /                                                                                                                                         /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                      |     ||         /                                                                                                                                                    /                                                                                                                                         /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                       /                                                                                                                                         /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                      |
         ||        /                                                                                                                                                    /                                                                                                                                         /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                                                                                                                      /                                                                                                                                         /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                      |     ||        /                                                                                                                                                    /                                                                                                                                         /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                                                                                                                      /                                                                                                                                         /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                      |
         ||       /                                                                                                                                                    /                                                                                                                                         /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                                                                                                                     /                                                                                                                                         /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                      |     ||       /                                                                                                                                                    /                                                                                                                                         /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                                                                                                                     /                                                                                                                                         /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                      |
         ||      /                                                                                                                                                    /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                                                                                                                    /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                      |     ||      /                                                                                                                                                    /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                                                                                                                    /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                      |
         ||    \/                                                                                                                                                   \/                                                                                                                                        \/         \/                        4                         27           27              3                                                                                                                           \/                                                                                                                                        \/         \/                        4                         27           27              3                               |     ||    \/                                                                                                                                                   \/                                                                                                                                        \/         \/                        4                         27           27              3                                                                                                                           \/                                                                                                                                        \/         \/                        4                         27           27              3                               |
         ||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------      otherwise     |     ||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------      otherwise     |
         ||                                                                                                                                                                                                                                                             2                                                                                                                                                                                                                                                                                                                                                                                     2                                                                                                                                             |     ||                                                                                                                                                                                                                                                             2                                                                                                                                                                                                                                                                                                                                                                                     2                                                                                                                                             |
         \\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /     \\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /
$$x_{2} = \operatorname{re}{\left(\begin{cases} y - \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} + \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y - \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} y - \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} + \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y - \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{- \frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
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         ||                                                                                                                                                                                                                                                                                                                                                                 /     2*3 /    - ------ - -------------------  + ----- + ----------------------------------------------------------                                                                                                                                                                                                                                                                                                             |     ||                                                                                                                                                                                                                                                                                                                                                                 /     2*3 /    - ------ - -------------------  + ----- + ----------------------------------------------------------                                                                                                                                                                                                                                                                                                             |
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         ||                                                                                                                                                                                                                                                                                              /     - 2*3 /    - ------ - -------------------  + ----      /                                                                /     - 2*3 /    - ------ - -------------------  + ----                                                                                                                                                                                                                                                                                                         4    |     ||                                                                                                                                                                                                                                                                                              /     - 2*3 /    - ------ - -------------------  + ----      /                                                                /     - 2*3 /    - ------ - -------------------  + ----                                                                                                                                                                                                                                                                                                         4    |
         ||                                                                                                                                                                                                                                                                                            \/          \/         27              3              3      \/                                                               \/          \/         27              3              3                                                                                                                                                                                                                                                                                                  4*y   8*y     |     ||                                                                                                                                                                                                                                                                                            \/          \/         27              3              3      \/                                                               \/          \/         27              3              3                                                                                                                                                                                                                                                                                                  4*y   8*y     |
         ||                                                                                                                                                                                                                                                                                        y + ---------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------                                                                                                                                                                                                                                                                                          for --- + ---- = 0|     ||                                                                                                                                                                                                                                                                                        y + ---------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------                                                                                                                                                                                                                                                                                          for --- + ---- = 0|
         ||                                                                                                                                                                                                                                                                                                                        2                                                                                             2                                                                                                                                                                                                                                                                                                                                                             5     3      |     ||                                                                                                                                                                                                                                                                                                                        2                                                                                             2                                                                                                                                                                                                                                                                                                                                                             5     3      |
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         ||                                                                                                                                                                                                                                                                                 /               /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                                                                                                                                                                                                                 |4*y   8*y |                                                                  |     ||                                                                                                                                                                                                                                                                                 /               /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                                                                                                                                                                                                                 |4*y   8*y |                                                                  |
         ||                                                                                                                                                                                                                                                                                /               /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|        2                                                                                                                             3                                                                                                                                                                        2*|--- + ----|                                                                  |     ||                                                                                                                                                                                                                                                                                /               /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|        2                                                                                                                             3                                                                                                                                                                        2*|--- + ----|                                                                  |
x3 = I*im|<                                                                                                                                                                                                                                                                               /               /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    16*y                                                                                                                          16*y                                                                                                                                                                           \ 5     3  /                                                                  | + re|<                                                                                                                                                                                                                                                                               /               /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    16*y                                                                                                                          16*y                                                                                                                                                                           \ 5     3  /                                                                  |
         ||                                                                                                                                                                                                                                                                              /         - 2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ----- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------                     |     ||                                                                                                                                                                                                                                                                              /         - 2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ----- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------                     |
         ||                        ______________________________________________________________________________________________________________________________________________________________________________________________________________________________                       /              \/         \/                        4                         27           27              3               3                         ______________________________________________________________________________________________________________________________________________________________________________________________________________________________               _____________________________________________________________________________________________                     |     ||                        ______________________________________________________________________________________________________________________________________________________________________________________________________________________________                       /              \/         \/                        4                         27           27              3               3                         ______________________________________________________________________________________________________________________________________________________________________________________________________________________________               _____________________________________________________________________________________________                     |
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         ||                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                        /                                                                                                                                                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                       |     ||                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                        /                                                                                                                                                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                       |
         ||                   /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                                /                                                                                                                                                    /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                        /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                      |     ||                   /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                                /                                                                                                                                                    /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                        /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                      |
         ||                  /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                               /                                                                                                                                                    /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                       /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                      |     ||                  /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                               /                                                                                                                                                    /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                       /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                      |
         ||                 /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                              /                                                                                                                                                    /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                      /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                      |     ||                 /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                              /                                                                                                                                                    /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                      /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                      |
         ||                /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                             /                                                                                                                                                    /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                 3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                      |     ||                /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                             /                                                                                                                                                    /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                 3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                      |
         ||               /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------               /                                                                                                                                                    /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------      \/         \/                        4                         27           27              3                               |     ||               /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------               /                                                                                                                                                    /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------      \/         \/                        4                         27           27              3                               |
         ||              /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________              /                                                                                                                                                    /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________                                                                                                                                  |     ||              /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________              /                                                                                                                                                    /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________                                                                                                                                  |
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         ||           /                                                                                                                                         /          /  /              2 /     4   4*y\\                3                                            /                                                                                                                                                    /                                                                                                                                         /          /  /              2 /     4   4*y\\                3                                                                                                                                                                   |     ||           /                                                                                                                                         /          /  /              2 /     4   4*y\\                3                                            /                                                                                                                                                    /                                                                                                                                         /          /  /              2 /     4   4*y\\                3                                                                                                                                                                   |
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         ||         /                                                                                                                                         /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\          /                                                                                                                                                    /                                                                                                                                         /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                                   |     ||         /                                                                                                                                         /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\          /                                                                                                                                                    /                                                                                                                                         /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                                   |
         ||        /                                                                                                                                         /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|         /                                                                                                                                                    /                                                                                                                                         /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                                                                                                                                   |     ||        /                                                                                                                                         /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|         /                                                                                                                                                    /                                                                                                                                         /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                                                                                                                                   |
         ||       /                                                                                                                                         /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /        /                                                                                                                                                    /                                                                                                                                         /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                                                                                                                                   |     ||       /                                                                                                                                         /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /        /                                                                                                                                                    /                                                                                                                                         /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                                                                                                                                   |
         ||      /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------       /                                                                                                                                                    /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                                                                                                                                   |     ||      /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------       /                                                                                                                                                    /                                                                                                                                     3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                                                                                                                                   |
         ||    \/                                                                                                                                        \/         \/                        4                         27           27              3              \/                                                                                                                                                   \/                                                                                                                                        \/         \/                        4                         27           27              3                                                                                                                                            |     ||    \/                                                                                                                                        \/         \/                        4                         27           27              3              \/                                                                                                                                                   \/                                                                                                                                        \/         \/                        4                         27           27              3                                                                                                                                            |
         ||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------      otherwise     |     ||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------      otherwise     |
         ||                                                                                                                            2                                                                                                                                                                                                                                                                                                                                                                                     2                                                                                                                                                                                                                                                                              |     ||                                                                                                                            2                                                                                                                                                                                                                                                                                                                                                                                     2                                                                                                                                                                                                                                                                              |
         \\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /     \\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /
$$x_{3} = \operatorname{re}{\left(\begin{cases} y + \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} - \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y + \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} y + \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} - \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y + \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} - \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
         //                                                                                                                                                                                                                                                                                                                                                                      _______________________________________________________________________________________________________________                                                                                                                                                                                                                                                                                                            \     //                                                                                                                                                                                                                                                                                                                                                                      _______________________________________________________________________________________________________________                                                                                                                                                                                                                                                                                                            \
         ||                                                                                                                                                                                                                                                                                                                                                                     /         ________________________________                                                                                                                                                                                                                                                                                                                                                                                  |     ||                                                                                                                                                                                                                                                                                                                                                                     /         ________________________________                                                                                                                                                                                                                                                                                                                                                                                  |
         ||                                                                                                                                                                                                                                                                                                                                                                    /         /               2 /     4   4*y\                                                                                                                                                                                                                                                                                                                                                                                   |     ||                                                                                                                                                                                                                                                                                                                                                                    /         /               2 /     4   4*y\                                                                                                                                                                                                                                                                                                                                                                                   |
         ||                                                                                                                                                                                                                                                                                                                                                                   /         /         6   4*y *|- 4*y  - ---|        2                                 3                                                                                                                                                                                                                                                                                                                                        |     ||                                                                                                                                                                                                                                                                                                                                                                   /         /         6   4*y *|- 4*y  - ---|        2                                 3                                                                                                                                                                                                                                                                                                                                        |
         ||                                                                                                                                                                                                                                                                                                                                                                  /         /     200*y         \          5 /    16*y                              16*y                                                                                                                                                                                                                                                                                                                                         |     ||                                                                                                                                                                                                                                                                                                                                                                  /         /     200*y         \          5 /    16*y                              16*y                                                                                                                                                                                                                                                                                                                                         |
         ||                                                                                                                                                                                                                                                                                                                                                                 /     2*3 /    - ------ - -------------------  + ----- + ----------------------------------------------------------                                                                                                                                                                                                                                                                                                             |     ||                                                                                                                                                                                                                                                                                                                                                                 /     2*3 /    - ------ - -------------------  + ----- + ----------------------------------------------------------                                                                                                                                                                                                                                                                                                             |
         ||                                                                                                                                                                                                                                                                                                   ___________________________________________________          /        \/         27              3               3            ___________________________________________________                                                                                                                                                                                                                                                                                                             |     ||                                                                                                                                                                                                                                                                                                   ___________________________________________________          /        \/         27              3               3            ___________________________________________________                                                                                                                                                                                                                                                                                                             |
         ||                                                                                                                                                                                                                                                                                                  /           ________________________________                 /                                                                /           ________________________________                                                                                                                                                                                                                                                                                                                     |     ||                                                                                                                                                                                                                                                                                                  /           ________________________________                 /                                                                /           ________________________________                                                                                                                                                                                                                                                                                                                     |
         ||                                                                                                                                                                                                                                                                                                 /           /               2 /     4   4*y\                 /                                                                /           /               2 /     4   4*y\                                                                                                                                                                                                                                                                                                                      |     ||                                                                                                                                                                                                                                                                                                 /           /               2 /     4   4*y\                 /                                                                /           /               2 /     4   4*y\                                                                                                                                                                                                                                                                                                                      |
         ||                                                                                                                                                                                                                                                                                                /           /         6   4*y *|- 4*y  - ---|       2        /                                                                /           /         6   4*y *|- 4*y  - ---|       2                                                                                                                                                                                                                                                                                                              |     ||                                                                                                                                                                                                                                                                                                /           /         6   4*y *|- 4*y  - ---|       2        /                                                                /           /         6   4*y *|- 4*y  - ---|       2                                                                                                                                                                                                                                                                                                              |
         ||                                                                                                                                                                                                                                                                                               /           /     200*y         \          5 /    8*y        /                                                                /           /     200*y         \          5 /    8*y                                                                                                                                                                                                                                                                                                               |     ||                                                                                                                                                                                                                                                                                               /           /     200*y         \          5 /    8*y        /                                                                /           /     200*y         \          5 /    8*y                                                                                                                                                                                                                                                                                                               |
         ||                                                                                                                                                                                                                                                                                              /     - 2*3 /    - ------ - -------------------  + ----      /                                                                /     - 2*3 /    - ------ - -------------------  + ----                                                                                                                                                                                                                                                                                                         4    |     ||                                                                                                                                                                                                                                                                                              /     - 2*3 /    - ------ - -------------------  + ----      /                                                                /     - 2*3 /    - ------ - -------------------  + ----                                                                                                                                                                                                                                                                                                         4    |
         ||                                                                                                                                                                                                                                                                                            \/          \/         27              3              3      \/                                                               \/          \/         27              3              3                                                                                                                                                                                                                                                                                                  4*y   8*y     |     ||                                                                                                                                                                                                                                                                                            \/          \/         27              3              3      \/                                                               \/          \/         27              3              3                                                                                                                                                                                                                                                                                                  4*y   8*y     |
         ||                                                                                                                                                                                                                                                                                        y + ---------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------                                                                                                                                                                                                                                                                                          for --- + ---- = 0|     ||                                                                                                                                                                                                                                                                                        y + ---------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------                                                                                                                                                                                                                                                                                          for --- + ---- = 0|
         ||                                                                                                                                                                                                                                                                                                                        2                                                                                             2                                                                                                                                                                                                                                                                                                                                                             5     3      |     ||                                                                                                                                                                                                                                                                                                                        2                                                                                             2                                                                                                                                                                                                                                                                                                                                                             5     3      |
         ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |     ||                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
         ||                                                                                                                                                                                                                                                                                       ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________                    |     ||                                                                                                                                                                                                                                                                                       ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________                    |
         ||                                                                                                                                                                                                                                                                                      /               _____________________________________________________________________________________________                                                                                                                                                                                                                                                                                                                                                                                              |     ||                                                                                                                                                                                                                                                                                      /               _____________________________________________________________________________________________                                                                                                                                                                                                                                                                                                                                                                                              |
         ||                                                                                                                                                                                                                                                                                     /               /          ___________________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                              |     ||                                                                                                                                                                                                                                                                                     /               /          ___________________________________________________                                                                                                                                                                                                                                                                                                                                                                                                                              |
         ||                                                                                                                                                                                                                                                                                    /               /          /                                 2                                                                                                                                                                                                                                                                                                                                                                                                                                               |     ||                                                                                                                                                                                                                                                                                    /               /          /                                 2                                                                                                                                                                                                                                                                                                                                                                                                                                               |
         ||                                                                                                                                                                                                                                                                                   /               /          /  /              2 /     4   4*y\\                3                                                                                                                                                                                                                                                                                                                                                                                                                               |     ||                                                                                                                                                                                                                                                                                   /               /          /  /              2 /     4   4*y\\                3                                                                                                                                                                                                                                                                                                                                                                                                                               |
         ||                                                                                                                                                                                                                                                                                  /               /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                                                                                                                                                                                                                                                                                  /         4\                                                                  |     ||                                                                                                                                                                                                                                                                                  /               /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                                                                                                                                                                                                                                                                                  /         4\                                                                  |
         ||                                                                                                                                                                                                                                                                                 /               /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                                                                                                                                                                                                                 |4*y   8*y |                                                                  |     ||                                                                                                                                                                                                                                                                                 /               /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                                                                                                                                                                                                                                                                                 |4*y   8*y |                                                                  |
         ||                                                                                                                                                                                                                                                                                /               /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|        2                                                                                                                             3                                                                                                                                                                        2*|--- + ----|                                                                  |     ||                                                                                                                                                                                                                                                                                /               /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|        2                                                                                                                             3                                                                                                                                                                        2*|--- + ----|                                                                  |
x4 = I*im|<                                                                                                                                                                                                                                                                               /               /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    16*y                                                                                                                          16*y                                                                                                                                                                           \ 5     3  /                                                                  | + re|<                                                                                                                                                                                                                                                                               /               /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    16*y                                                                                                                          16*y                                                                                                                                                                           \ 5     3  /                                                                  |
         ||                                                                                                                                                                                                                                                                              /         - 2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ----- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------                     |     ||                                                                                                                                                                                                                                                                              /         - 2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ----- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------                     |
         ||                        ______________________________________________________________________________________________________________________________________________________________________________________________________________________________                       /              \/         \/                        4                         27           27              3               3                         ______________________________________________________________________________________________________________________________________________________________________________________________________________________________               _____________________________________________________________________________________________                     |     ||                        ______________________________________________________________________________________________________________________________________________________________________________________________________________________________                       /              \/         \/                        4                         27           27              3               3                         ______________________________________________________________________________________________________________________________________________________________________________________________________________________________               _____________________________________________________________________________________________                     |
         ||                       /             _____________________________________________________________________________________________                                                                                                                                          /                                                                                                                                                    /             _____________________________________________________________________________________________                                                                                                                                  /          ___________________________________________________                                                     |     ||                       /             _____________________________________________________________________________________________                                                                                                                                          /                                                                                                                                                    /             _____________________________________________________________________________________________                                                                                                                                  /          ___________________________________________________                                                     |
         ||                      /             /          ___________________________________________________                                                                                                                                                                         /                                                                                                                                                    /             /          ___________________________________________________                                                                                                                                                                 /          /                                 2                                                                      |     ||                      /             /          ___________________________________________________                                                                                                                                                                         /                                                                                                                                                    /             /          ___________________________________________________                                                                                                                                                                 /          /                                 2                                                                      |
         ||                     /             /          /                                 2                                                                                                                                                                                         /                                                                                                                                                    /             /          /                                 2                                                                                                                                                                                 /          /  /              2 /     4   4*y\\                3                                                      |     ||                     /             /          /                                 2                                                                                                                                                                                         /                                                                                                                                                    /             /          /                                 2                                                                                                                                                                                 /          /  /              2 /     4   4*y\\                3                                                      |
         ||                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                        /                                                                                                                                                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                       |     ||                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                        /                                                                                                                                                    /             /          /  /              2 /     4   4*y\\                3                                                                                                                                                                /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                       |
         ||                   /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                                /                                                                                                                                                    /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                        /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                      |     ||                   /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                                /                                                                                                                                                    /             /          /   |       6   4*y *|- 4*y  - ---||    /         4\                                                                                            /         4\                                                        /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                      |
         ||                  /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                               /                                                                                                                                                    /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                       /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                      |     ||                  /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                               /                                                                                                                                                    /             /          /    |  200*y         \          5 /|    |4*y   8*y |                 2 /     4   4*y\                                                           |4*y   8*y |                                                       /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|                      |
         ||                 /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                              /                                                                                                                                                    /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                      /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                      |     ||                 /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                              /                                                                                                                                                    /             /          /     |- ------ - -------------------|    |--- + ----|          6   2*y *|- 4*y  - ---|       2                                                 2*|--- + ----|                                                      /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /                      |
         ||                /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                             /                                                                                                                                                    /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                 3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                      |     ||                /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                             /                                                                                                                                                    /             /          /      \    27              3         /    \ 5     3  /     100*y         \          5 /    8*y                                                    \ 5     3  /                                                 3*3 /          /       --------------------------------- + -------------  + ------ + -------------------                      |
         ||               /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------               /                                                                                                                                                    /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------      \/         \/                        4                         27           27              3                               |     ||               /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------               /                                                                                                                                                    /         2*3 /          /       --------------------------------- + -------------  + ------ + -------------------  + ---- - ---------------------------------------------------------------------------------------------------------      \/         \/                        4                         27           27              3                               |
         ||              /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________              /                                                                                                                                                    /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________                                                                                                                                  |     ||              /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________              /                                                                                                                                                    /            \/         \/                        4                         27           27              3              3                 _____________________________________________________________________________________________                                                                                                                                  |
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         ||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------      otherwise     |     ||y + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------      otherwise     |
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$$x_{4} = \operatorname{re}{\left(\begin{cases} y + \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} + \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y + \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} y + \frac{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} + \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}} + \frac{16 y^{2}}{3} + 2 \sqrt[3]{- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}}}}{2} & \text{for}\: \frac{8 y^{4}}{3} + \frac{4 y}{5} = 0 \\y + \frac{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} + \frac{\sqrt{\frac{16 y^{3}}{\sqrt{\frac{8 y^{2}}{3} - \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} + 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}} + \frac{16 y^{2}}{3} + \frac{2 \left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)}{3 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}} - 2 \sqrt[3]{\frac{100 y^{6}}{27} + \frac{2 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3} + \sqrt{\frac{\left(\frac{8 y^{4}}{3} + \frac{4 y}{5}\right)^{3}}{27} + \frac{\left(- \frac{200 y^{6}}{27} - \frac{4 y^{2} \left(- 4 y^{4} - \frac{4 y}{5}\right)}{3}\right)^{2}}{4}}}}}{2} & \text{otherwise} \end{cases}\right)}$$
x4 = re(Piecewise((y + sqrt(8*y^2/3 - 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3))/2 + sqrt(16*y^3/sqrt(8*y^2/3 - 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3)) + 16*y^2/3 + 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3)/2, 8*y^4/3 + 4*y/5 = 0), (y + sqrt(8*y^2/3 - 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3))/2 + sqrt(16*y^3/sqrt(8*y^2/3 - 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 16*y^2/3 + 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) - 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3))/2, True))) + i*im(Piecewise((y + sqrt(8*y^2/3 - 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3))/2 + sqrt(16*y^3/sqrt(8*y^2/3 - 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3)) + 16*y^2/3 + 2*(-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^(1/3))/2, 8*y^4/3 + 4*y/5 = 0), (y + sqrt(8*y^2/3 - 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3))/2 + sqrt(16*y^3/sqrt(8*y^2/3 - 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) + 16*y^2/3 + 2*(8*y^4/3 + 4*y/5)/(3*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3)) - 2*(100*y^6/27 + 2*y^2*(-4*y^4 - 4*y/5)/3 + sqrt((8*y^4/3 + 4*y/5)^3/27 + (-200*y^6/27 - 4*y^2*(-4*y^4 - 4*y/5)/3)^2/4))^(1/3))/2, True))))