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sqr(7x+1)+sqr(3x-18)=sqr(2x+7) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                    4            2
7*x + 1 + (3*x - 18)  = (2*x + 7)
$$\left(3 x - 18\right)^{4} + \left(7 x + 1\right) = \left(2 x + 7\right)^{2}$$
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Suma y producto de raíces [src] 
suma
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                                                                                                                            /   | 16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                  |                                                                                                                                /   | 16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                  |                                                                                                                              /    16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                                                                                                                                                /    16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                   
                                                                                                              I*           /    |--- - 2*3 /   --------- + ------------------  - ---------------------------------------------------------------------------------------------------------- + -------------------------------------------|                                                                                                                  I*           /    |--- - 2*3 /   --------- + ------------------  - ---------------------------------------------------------------------------------------------------------- + -------------------------------------------|                                                                                                                             /    --- - 2*3 /   --------- + ------------------  + ---------------------------------------------------------------------------------------------------------- + -------------------------------------------                                                                                                                             /    --- - 2*3 /   --------- + ------------------  + ---------------------------------------------------------------------------------------------------------- + ------------------------------------------- 
              _____________________________________________________________________________________________               /     |243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________|                  _____________________________________________________________________________________________               /     |243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________|                  _____________________________________________________________________________________________             /     243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________                  _____________________________________________________________________________________________             /     243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________ 
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           /    8         /   2993875    5*\/ 720104647345                        154540                               /        |                                                          /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------ |               /    8         /   2993875    5*\/ 720104647345                        154540                               /        |                                                          /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------ |               /    8         /   2993875    5*\/ 720104647345                        154540                             /                                                                  /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------                /    8         /   2993875    5*\/ 720104647345                        154540                             /                                                                  /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------  
          /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------            /         |                                                27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352       |              /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------            /         |                                                27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352       |              /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          /                                                         27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352                     /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          /                                                         27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352        
         /     243     \/    229582512        2834352                     ________________________________           /          |                                                        /     243     \/    229582512        2834352                     ________________________________                                               |             /     243     \/    229582512        2834352                     ________________________________           /          |                                                        /     243     \/    229582512        2834352                     ________________________________                                               |             /     243     \/    229582512        2834352                     ________________________________         /                                                                  /     243     \/    229582512        2834352                     ________________________________                                                            /     243     \/    229582512        2834352                     ________________________________         /                                                                  /     243     \/    229582512        2834352                     ________________________________                                                
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       /                                                                /   2993875    5*\/ 720104647345           /            |                                                      /                                                                /   2993875    5*\/ 720104647345                                                 |           /                                                                /   2993875    5*\/ 720104647345           /            |                                                      /                                                                /   2993875    5*\/ 720104647345                                                 |           /                                                                /   2993875    5*\/ 720104647345         /                                                                  /                                                                /   2993875    5*\/ 720104647345                                                            /                                                                /   2993875    5*\/ 720104647345         /                                                                  /                                                                /   2993875    5*\/ 720104647345                                                  
      /                                                        59049*3 /   --------- + ------------------         /             |                                                     /                                                        59049*3 /   --------- + ------------------                                                |          /                                                        59049*3 /   --------- + ------------------         /             |                                                     /                                                        59049*3 /   --------- + ------------------                                                |          /                                                        59049*3 /   --------- + ------------------       /                                                                  /                                                        59049*3 /   --------- + ------------------                                                          /                                                        59049*3 /   --------- + ------------------       /                                                                  /                                                        59049*3 /   --------- + ------------------                                                 
    \/                                                               \/    229582512        2834352             \/              |                                                   \/                                                               \/    229582512        2834352                                                      |        \/                                                               \/    229582512        2834352             \/              |                                                   \/                                                               \/    229582512        2834352                                                      |        \/                                                               \/    229582512        2834352           \/                                                                 \/                                                               \/    229582512        2834352                                                              \/                                                               \/    229582512        2834352           \/                                                                 \/                                                               \/    229582512        2834352                                                       
6 - ------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 6 - ------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 6 + ------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 6 + ------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                       2                                                                                                                                                                    2                                                                                                                                                                        2                                                                                                                                                                    2                                                                                                                                                                        2                                                                                                                                                                  2                                                                                                                                                                      2                                                                                                                                                                  2
$$\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}}}{2} + \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + 6\right) + \left(\left(\frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}}}{2} + 6\right) + \left(\left(- \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + 6 - \frac{i \sqrt{\left|{- \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}} - 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}\right|}}{2}\right) + \left(- \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + 6 + \frac{i \sqrt{\left|{- \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}} - 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}\right|}}{2}\right)\right)\right)$$ 
=
24
$$24$$ 
producto
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|                                                                                                                            /   | 16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                  | | |                                                                                                                            /   | 16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                  | | |                                                                                                                          /    16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                   | |                                                                                                                          /    16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                   |
|                                                                                                              I*           /    |--- - 2*3 /   --------- + ------------------  - ---------------------------------------------------------------------------------------------------------- + -------------------------------------------| | |                                                                                                              I*           /    |--- - 2*3 /   --------- + ------------------  - ---------------------------------------------------------------------------------------------------------- + -------------------------------------------| | |                                                                                                                         /    --- - 2*3 /   --------- + ------------------  + ---------------------------------------------------------------------------------------------------------- + ------------------------------------------- | |                                                                                                                         /    --- - 2*3 /   --------- + ------------------  + ---------------------------------------------------------------------------------------------------------- + ------------------------------------------- |
|              _____________________________________________________________________________________________               /     |243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________| | |              _____________________________________________________________________________________________               /     |243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________| | |              _____________________________________________________________________________________________             /     243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________ | |              _____________________________________________________________________________________________             /     243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________ |
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|            /              /                 ______________                                                             /       |                                                           /              /                 ______________                                                            /   2993875    5*\/ 720104647345  | | |            /              /                 ______________                                                             /       |                                                           /              /                 ______________                                                            /   2993875    5*\/ 720104647345  | | |            /              /                 ______________                                                           /                                                                  /              /                 ______________                                                            /   2993875    5*\/ 720104647345   | |            /              /                 ______________                                                           /                                                                  /              /                 ______________                                                            /   2993875    5*\/ 720104647345   |
|           /    8         /   2993875    5*\/ 720104647345                        154540                               /        |                                                          /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------ | | |           /    8         /   2993875    5*\/ 720104647345                        154540                               /        |                                                          /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------ | | |           /    8         /   2993875    5*\/ 720104647345                        154540                             /                                                                  /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------  | |           /    8         /   2993875    5*\/ 720104647345                        154540                             /                                                                  /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------  |
|          /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------            /         |                                                27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352       | | |          /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------            /         |                                                27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352       | | |          /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          /                                                         27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352        | |          /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          /                                                         27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352        |
|         /     243     \/    229582512        2834352                     ________________________________           /          |                                                        /     243     \/    229582512        2834352                     ________________________________                                               | | |         /     243     \/    229582512        2834352                     ________________________________           /          |                                                        /     243     \/    229582512        2834352                     ________________________________                                               | | |         /     243     \/    229582512        2834352                     ________________________________         /                                                                  /     243     \/    229582512        2834352                     ________________________________                                                | |         /     243     \/    229582512        2834352                     ________________________________         /                                                                  /     243     \/    229582512        2834352                     ________________________________                                                |
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|       /                                                                /   2993875    5*\/ 720104647345           /            |                                                      /                                                                /   2993875    5*\/ 720104647345                                                 | | |       /                                                                /   2993875    5*\/ 720104647345           /            |                                                      /                                                                /   2993875    5*\/ 720104647345                                                 | | |       /                                                                /   2993875    5*\/ 720104647345         /                                                                  /                                                                /   2993875    5*\/ 720104647345                                                  | |       /                                                                /   2993875    5*\/ 720104647345         /                                                                  /                                                                /   2993875    5*\/ 720104647345                                                  |
|      /                                                        59049*3 /   --------- + ------------------         /             |                                                     /                                                        59049*3 /   --------- + ------------------                                                | | |      /                                                        59049*3 /   --------- + ------------------         /             |                                                     /                                                        59049*3 /   --------- + ------------------                                                | | |      /                                                        59049*3 /   --------- + ------------------       /                                                                  /                                                        59049*3 /   --------- + ------------------                                                 | |      /                                                        59049*3 /   --------- + ------------------       /                                                                  /                                                        59049*3 /   --------- + ------------------                                                 |
|    \/                                                               \/    229582512        2834352             \/              |                                                   \/                                                               \/    229582512        2834352                                                      | | |    \/                                                               \/    229582512        2834352             \/              |                                                   \/                                                               \/    229582512        2834352                                                      | | |    \/                                                               \/    229582512        2834352           \/                                                                 \/                                                               \/    229582512        2834352                                                       | |    \/                                                               \/    229582512        2834352           \/                                                                 \/                                                               \/    229582512        2834352                                                       |
|6 - ------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|6 - ------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|6 + ------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|6 + ------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\                                                       2                                                                                                                                                                    2                                                                                                              / \                                                       2                                                                                                                                                                    2                                                                                                              / \                                                       2                                                                                                                                                                  2                                                                                                            / \                                                       2                                                                                                                                                                  2                                                                                                            /
$$\left(- \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + 6 - \frac{i \sqrt{\left|{- \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}} - 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}\right|}}{2}\right) \left(- \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + 6 + \frac{i \sqrt{\left|{- \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}} - 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}\right|}}{2}\right) \left(\frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}}}{2} + 6\right) \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}}}{2} + \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + 6\right)$$ 
=
34976
-----
  27
$$\frac{34976}{27}$$ 
34976/27
Respuesta rápida [src] 
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                                                                                                                                 /   | 16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                  | 
                                                                                                                   I*           /    |--- - 2*3 /   --------- + ------------------  - ---------------------------------------------------------------------------------------------------------- + -------------------------------------------| 
                   _____________________________________________________________________________________________               /     |243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________| 
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                 /              /                 ______________                                                             /       |                                                           /              /                 ______________                                                            /   2993875    5*\/ 720104647345  | 
                /    8         /   2993875    5*\/ 720104647345                        154540                               /        |                                                          /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------ | 
               /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------            /         |                                                27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352       | 
              /     243     \/    229582512        2834352                     ________________________________           /          |                                                        /     243     \/    229582512        2834352                     ________________________________                                               | 
             /                                                                /                 ______________           /           |                                                       /                                                                /                 ______________                                                | 
            /                                                                /   2993875    5*\/ 720104647345           /            |                                                      /                                                                /   2993875    5*\/ 720104647345                                                 | 
           /                                                        59049*3 /   --------- + ------------------         /             |                                                     /                                                        59049*3 /   --------- + ------------------                                                | 
         \/                                                               \/    229582512        2834352             \/              |                                                   \/                                                               \/    229582512        2834352                                                      | 
x1 = 6 - ------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                            2                                                                                                                                                                    2
$$x_{1} = - \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + 6 - \frac{i \sqrt{\left|{- \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}} - 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}\right|}}{2}$$ 
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                                                                                                                                  /  |            /                 ______________                                                                                                                                                            | 
                                                                                                                                 /   | 16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                  | 
                                                                                                                   I*           /    |--- - 2*3 /   --------- + ------------------  - ---------------------------------------------------------------------------------------------------------- + -------------------------------------------| 
                   _____________________________________________________________________________________________               /     |243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________| 
                  /              ________________________________                                                             /      |                                                            /              ________________________________                                                            /                 ______________ | 
                 /              /                 ______________                                                             /       |                                                           /              /                 ______________                                                            /   2993875    5*\/ 720104647345  | 
                /    8         /   2993875    5*\/ 720104647345                        154540                               /        |                                                          /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------ | 
               /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------            /         |                                                27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352       | 
              /     243     \/    229582512        2834352                     ________________________________           /          |                                                        /     243     \/    229582512        2834352                     ________________________________                                               | 
             /                                                                /                 ______________           /           |                                                       /                                                                /                 ______________                                                | 
            /                                                                /   2993875    5*\/ 720104647345           /            |                                                      /                                                                /   2993875    5*\/ 720104647345                                                 | 
           /                                                        59049*3 /   --------- + ------------------         /             |                                                     /                                                        59049*3 /   --------- + ------------------                                                | 
         \/                                                               \/    229582512        2834352             \/              |                                                   \/                                                               \/    229582512        2834352                                                      | 
x2 = 6 - ------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                            2                                                                                                                                                                    2
$$x_{2} = - \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + 6 + \frac{i \sqrt{\left|{- \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}} - 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}\right|}}{2}$$ 
                                                                                                                                  __________________________________________________________________________________________________________________________________________________________________________________________________________
                                                                                                                                 /              ________________________________                                                                                                                                                            
                                                                                                                                /              /                 ______________                                                                                                                                                             
                                                                                                                               /    16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                   
                                                                                                                              /    --- - 2*3 /   --------- + ------------------  + ---------------------------------------------------------------------------------------------------------- + ------------------------------------------- 
                   _____________________________________________________________________________________________             /     243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________ 
                  /              ________________________________                                                           /                                                                  /              ________________________________                                                            /                 ______________  
                 /              /                 ______________                                                           /                                                                  /              /                 ______________                                                            /   2993875    5*\/ 720104647345   
                /    8         /   2993875    5*\/ 720104647345                        154540                             /                                                                  /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------  
               /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          /                                                         27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352        
              /     243     \/    229582512        2834352                     ________________________________         /                                                                  /     243     \/    229582512        2834352                     ________________________________                                                
             /                                                                /                 ______________         /                                                                  /                                                                /                 ______________                                                 
            /                                                                /   2993875    5*\/ 720104647345         /                                                                  /                                                                /   2993875    5*\/ 720104647345                                                  
           /                                                        59049*3 /   --------- + ------------------       /                                                                  /                                                        59049*3 /   --------- + ------------------                                                 
         \/                                                               \/    229582512        2834352           \/                                                                 \/                                                               \/    229582512        2834352                                                       
x3 = 6 + ------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                            2                                                                                                                                                                  2
$$x_{3} = \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}}}{2} + 6$$ 
                                                                                                                                  __________________________________________________________________________________________________________________________________________________________________________________________________________
                                                                                                                                 /              ________________________________                                                                                                                                                            
                                                                                                                                /              /                 ______________                                                                                                                                                             
                                                                                                                               /    16        /   2993875    5*\/ 720104647345                                                         46                                                                          154540                   
                                                                                                                              /    --- - 2*3 /   --------- + ------------------  + ---------------------------------------------------------------------------------------------------------- + ------------------------------------------- 
                   _____________________________________________________________________________________________             /     243     \/    229582512        2834352                       _____________________________________________________________________________________________              ________________________________ 
                  /              ________________________________                                                           /                                                                  /              ________________________________                                                            /                 ______________  
                 /              /                 ______________                                                           /                                                                  /              /                 ______________                                                            /   2993875    5*\/ 720104647345   
                /    8         /   2993875    5*\/ 720104647345                        154540                             /                                                                  /    8         /   2993875    5*\/ 720104647345                        154540                      59049*3 /   --------- + ------------------  
               /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          /                                                         27*      /    --- + 2*3 /   --------- + ------------------  - -------------------------------------------          \/    229582512        2834352        
              /     243     \/    229582512        2834352                     ________________________________         /                                                                  /     243     \/    229582512        2834352                     ________________________________                                                
             /                                                                /                 ______________         /                                                                  /                                                                /                 ______________                                                 
            /                                                                /   2993875    5*\/ 720104647345         /                                                                  /                                                                /   2993875    5*\/ 720104647345                                                  
           /                                                        59049*3 /   --------- + ------------------       /                                                                  /                                                        59049*3 /   --------- + ------------------                                                 
         \/                                                               \/    229582512        2834352           \/                                                                 \/                                                               \/    229582512        2834352                                                       
x4 = 6 + ------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                            2                                                                                                                                                                  2
$$x_{4} = - \frac{\sqrt{- 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}} + \frac{16}{243} + \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{46}{27 \sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}}}{2} + \frac{\sqrt{- \frac{154540}{59049 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}} + \frac{8}{243} + 2 \sqrt[3]{\frac{2993875}{229582512} + \frac{5 \sqrt{720104647345}}{2834352}}}}{2} + 6$$ 
x4 = -sqrt(-2*(2993875/229582512 + 5*sqrt(720104647345)/2834352)^(1/3) + 16/243 + 154540/(59049*(2993875/229582512 + 5*sqrt(720104647345)/2834352)^(1/3)) + 46/(27*sqrt(-154540/(59049*(2993875/229582512 + 5*sqrt(720104647345)/2834352)^(1/3)) + 8/243 + 2*(2993875/229582512 + 5*sqrt(720104647345)/2834352)^(1/3))))/2 + sqrt(-154540/(59049*(2993875/229582512 + 5*sqrt(720104647345)/2834352)^(1/3)) + 8/243 + 2*(2993875/229582512 + 5*sqrt(720104647345)/2834352)^(1/3))/2 + 6
Respuesta numérica [src] 
x1 = 5.89251870493718 - 1.40294563354997*i
x2 = 5.89251870493718 + 1.40294563354997*i
x3 = 4.69520132665374
x4 = 7.51976126347189
x4 = 7.51976126347189
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