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(x-2)*(x-4)*(x-7)=x la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
(x - 2)*(x - 4)*(x - 7) = x
$$\left(x - 4\right) \left(x - 2\right) \left(x - 7\right) = x$$
Gráfica
Suma y producto de raíces [src]
suma
          /                   1                   \     /     /                   1                   \                                                              \                                                                           /                   1                   \     /     /                   1                   \                                                              \                                                                                                                         
     22*re|---------------------------------------|     |22*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\        22*re|---------------------------------------|     |22*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\                                                           
          |                     __________________|     |     |                     __________________|             |    |3*\/ 1407 ||             |    |3*\/ 1407 |||             |    |3*\/ 1407 ||             |    |3*\/ 1407 ||             |                     __________________|     |     |                     __________________|             |    |3*\/ 1407 ||             |    |3*\/ 1407 |||             |    |3*\/ 1407 ||             |    |3*\/ 1407 ||                                                           
          |/          ___\     /           ______ |     |     |/          ___\     /           ______ |             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||             |/          ___\     /           ______ |     |     |/          ___\     /           ______ |             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||                                                           
          ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     |     ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     ____    |    \   173    /|     ____    |    \   173    /||     ____    |    \   173    /|     ____    |    \   173    /|             ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     |     ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     ____    |    \   173    /|     ____    |    \   173    /||     ____    |    \   173    /|     ____    |    \   173    /|             __________________                            
          ||- - - -------|*3 /   --- + ---------- |     |     ||- - - -------|*3 /   --- + ---------- |   \/ 22 *sin|----------------|   \/ 66 *cos|----------------||   \/ 22 *cos|----------------|   \/ 66 *sin|----------------|             ||- - + -------|*3 /   --- + ---------- |     |     ||- - + -------|*3 /   --- + ---------- |   \/ 22 *sin|----------------|   \/ 66 *cos|----------------||   \/ 22 *cos|----------------|   \/ 66 *sin|----------------|            /           ______                             
13        \\  2      2   / \/     54       18     /     |     \\  2      2   / \/     54       18     /             \       3        /             \       3        /|             \       3        /             \       3        /   13        \\  2      2   / \/     54       18     /     |     \\  2      2   / \/     54       18     /             \       3        /             \       3        /|             \       3        /             \       3        /   13      /  173   I*\/ 1407                 22           
-- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- - ----------------------------| - ---------------------------- + ---------------------------- + -- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + ----------------------------| - ---------------------------- - ---------------------------- + -- + 3 /   --- + ----------  + -------------------------
3                          9                            \                      9                                       6                              6              /                6                              6                 3                          9                            \                      9                                       6                              6              /                6                              6                 3    \/     54       18               __________________
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /           ______ 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  /  173   I*\/ 1407  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             9*3 /   --- + ---------- 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \/     54       18     
$$\left(\frac{13}{3} + \frac{22}{9 \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}} + \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}\right) + \left(\left(\frac{22 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} - \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} - \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{13}{3} + i \left(\frac{22 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} - \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6}\right)\right) + \left(- \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{22 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{13}{3} + i \left(- \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} - \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{22 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9}\right)\right)\right)$$
=
                                                                /                   1                   \        /                   1                   \     /     /                   1                   \                                                              \     /     /                   1                   \                                                              \                               
                                                           22*re|---------------------------------------|   22*re|---------------------------------------|     |22*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|     |22*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\
                                                                |                     __________________|        |                     __________________|     |     |                     __________________|             |    |3*\/ 1407 ||             |    |3*\/ 1407 |||     |     |                     __________________|             |    |3*\/ 1407 ||             |    |3*\/ 1407 |||             |    |3*\/ 1407 ||
                                                                |/          ___\     /           ______ |        |/          ___\     /           ______ |     |     |/          ___\     /           ______ |             |atan|----------||             |atan|----------|||     |     |/          ___\     /           ______ |             |atan|----------||             |atan|----------|||             |atan|----------||
          __________________                                    ||  1   I*\/ 3 |    /  173   I*\/ 1407  |        ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     |     ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     ____    |    \   173    /|     ____    |    \   173    /||     |     ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     ____    |    \   173    /|     ____    |    \   173    /||     ____    |    \   173    /|
         /           ______                                     ||- - + -------|*3 /   --- + ---------- |        ||- - - -------|*3 /   --- + ---------- |     |     ||- - + -------|*3 /   --- + ---------- |   \/ 22 *sin|----------------|   \/ 66 *cos|----------------||     |     ||- - - -------|*3 /   --- + ---------- |   \/ 22 *sin|----------------|   \/ 66 *cos|----------------||   \/ 22 *cos|----------------|
        /  173   I*\/ 1407                 22                   \\  2      2   / \/     54       18     /        \\  2      2   / \/     54       18     /     |     \\  2      2   / \/     54       18     /             \       3        /             \       3        /|     |     \\  2      2   / \/     54       18     /             \       3        /             \       3        /|             \       3        /
13 + 3 /   --- + ----------  + ------------------------- + ---------------------------------------------- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + ----------------------------| + I*|---------------------------------------------- - ---------------------------- - ----------------------------| - ----------------------------
     \/     54       18               __________________                         9                                                9                            \                      9                                       6                              6              /     \                      9                                       6                              6              /                3              
                                     /           ______                                                                                                                                                                                                                                                                                                                                                                        
                                    /  173   I*\/ 1407                                                                                                                                                                                                                                                                                                                                                                         
                               9*3 /   --- + ----------                                                                                                                                                                                                                                                                                                                                                                        
                                 \/     54       18                                                                                                                                                                                                                                                                                                                                                                            
$$- \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{3} + \frac{22 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} + \frac{22 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} + 13 + \frac{22}{9 \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}} + i \left(\frac{22 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} - \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6}\right) + i \left(- \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} - \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{22 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9}\right) + \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}$$
producto
/          /                   1                   \     /     /                   1                   \                                                              \                                                              \ /          /                   1                   \     /     /                   1                   \                                                              \                                                              \                                                           
|     22*re|---------------------------------------|     |22*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\| |     22*re|---------------------------------------|     |22*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\|                                                           
|          |                     __________________|     |     |                     __________________|             |    |3*\/ 1407 ||             |    |3*\/ 1407 |||             |    |3*\/ 1407 ||             |    |3*\/ 1407 ||| |          |                     __________________|     |     |                     __________________|             |    |3*\/ 1407 ||             |    |3*\/ 1407 |||             |    |3*\/ 1407 ||             |    |3*\/ 1407 |||                                                           
|          |/          ___\     /           ______ |     |     |/          ___\     /           ______ |             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||| |          |/          ___\     /           ______ |     |     |/          ___\     /           ______ |             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------|||                                                           
|          ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     |     ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     ____    |    \   173    /|     ____    |    \   173    /||     ____    |    \   173    /|     ____    |    \   173    /|| |          ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     |     ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     ____    |    \   173    /|     ____    |    \   173    /||     ____    |    \   173    /|     ____    |    \   173    /|| /          __________________                            \
|          ||- - - -------|*3 /   --- + ---------- |     |     ||- - - -------|*3 /   --- + ---------- |   \/ 22 *sin|----------------|   \/ 66 *cos|----------------||   \/ 22 *cos|----------------|   \/ 66 *sin|----------------|| |          ||- - + -------|*3 /   --- + ---------- |     |     ||- - + -------|*3 /   --- + ---------- |   \/ 22 *sin|----------------|   \/ 66 *cos|----------------||   \/ 22 *cos|----------------|   \/ 66 *sin|----------------|| |         /           ______                             |
|13        \\  2      2   / \/     54       18     /     |     \\  2      2   / \/     54       18     /             \       3        /             \       3        /|             \       3        /             \       3        /| |13        \\  2      2   / \/     54       18     /     |     \\  2      2   / \/     54       18     /             \       3        /             \       3        /|             \       3        /             \       3        /| |13      /  173   I*\/ 1407                 22           |
|-- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- - ----------------------------| - ---------------------------- + ----------------------------|*|-- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + ----------------------------| - ---------------------------- - ----------------------------|*|-- + 3 /   --- + ----------  + -------------------------|
\3                          9                            \                      9                                       6                              6              /                6                              6              / \3                          9                            \                      9                                       6                              6              /                6                              6              / |3    \/     54       18               __________________|
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                     /           ______ |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                    /  173   I*\/ 1407  |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                               9*3 /   --- + ---------- |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \                                 \/     54       18     /
$$\left(- \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{22 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{13}{3} + i \left(- \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} - \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{22 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9}\right)\right) \left(\frac{22 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} - \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} - \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{13}{3} + i \left(\frac{22 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} - \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6}\right)\right) \left(\frac{13}{3} + \frac{22}{9 \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}} + \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}\right)$$
=
                                                                         /            /      /    ______\\                /    /    ______\\\
                                                                         |            |      |3*\/ 1407 ||                |    |3*\/ 1407 |||
/              ____________________ /             ____________________\\ |            |2*atan|----------||                |atan|----------|||
|   3 ___   3 /             ______  |      2/3 3 /             ______ || |            |      \   173    /|        ____    |    \   173    /||
\44*\/ 2  + \/  173 + 3*I*\/ 1407  *\26 + 2   *\/  173 + 3*I*\/ 1407  //*|147 + 44*cos|------------------| - 26*\/ 22 *cos|----------------||
                                                                         \            \        3         /                \       3        //
---------------------------------------------------------------------------------------------------------------------------------------------
                                                                ____________________                                                         
                                                             3 /             ______                                                          
                                                          54*\/  173 + 3*I*\/ 1407                                                           
$$\frac{\left(44 \sqrt[3]{2} + \left(26 + 2^{\frac{2}{3}} \sqrt[3]{173 + 3 \sqrt{1407} i}\right) \sqrt[3]{173 + 3 \sqrt{1407} i}\right) \left(- 26 \sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)} + 44 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)} + 147\right)}{54 \sqrt[3]{173 + 3 \sqrt{1407} i}}$$
(44*2^(1/3) + (173 + 3*i*sqrt(1407))^(1/3)*(26 + 2^(2/3)*(173 + 3*i*sqrt(1407))^(1/3)))*(147 + 44*cos(2*atan(3*sqrt(1407)/173)/3) - 26*sqrt(22)*cos(atan(3*sqrt(1407)/173)/3))/(54*(173 + 3*i*sqrt(1407))^(1/3))
Respuesta rápida [src]
               /                   1                   \     /     /                   1                   \                                                              \                                                              
          22*re|---------------------------------------|     |22*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\
               |                     __________________|     |     |                     __________________|             |    |3*\/ 1407 ||             |    |3*\/ 1407 |||             |    |3*\/ 1407 ||             |    |3*\/ 1407 ||
               |/          ___\     /           ______ |     |     |/          ___\     /           ______ |             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||
               ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     |     ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     ____    |    \   173    /|     ____    |    \   173    /||     ____    |    \   173    /|     ____    |    \   173    /|
               ||- - - -------|*3 /   --- + ---------- |     |     ||- - - -------|*3 /   --- + ---------- |   \/ 22 *sin|----------------|   \/ 66 *cos|----------------||   \/ 22 *cos|----------------|   \/ 66 *sin|----------------|
     13        \\  2      2   / \/     54       18     /     |     \\  2      2   / \/     54       18     /             \       3        /             \       3        /|             \       3        /             \       3        /
x1 = -- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- - ----------------------------| - ---------------------------- + ----------------------------
     3                          9                            \                      9                                       6                              6              /                6                              6              
$$x_{1} = - \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{22 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} + \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{13}{3} + i \left(- \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} - \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{22 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9}\right)$$
               /                   1                   \     /     /                   1                   \                                                              \                                                              
          22*re|---------------------------------------|     |22*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\
               |                     __________________|     |     |                     __________________|             |    |3*\/ 1407 ||             |    |3*\/ 1407 |||             |    |3*\/ 1407 ||             |    |3*\/ 1407 ||
               |/          ___\     /           ______ |     |     |/          ___\     /           ______ |             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||
               ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     |     ||  1   I*\/ 3 |    /  173   I*\/ 1407  |     ____    |    \   173    /|     ____    |    \   173    /||     ____    |    \   173    /|     ____    |    \   173    /|
               ||- - + -------|*3 /   --- + ---------- |     |     ||- - + -------|*3 /   --- + ---------- |   \/ 22 *sin|----------------|   \/ 66 *cos|----------------||   \/ 22 *cos|----------------|   \/ 66 *sin|----------------|
     13        \\  2      2   / \/     54       18     /     |     \\  2      2   / \/     54       18     /             \       3        /             \       3        /|             \       3        /             \       3        /
x2 = -- + ---------------------------------------------- + I*|---------------------------------------------- - ---------------------------- + ----------------------------| - ---------------------------- - ----------------------------
     3                          9                            \                      9                                       6                              6              /                6                              6              
$$x_{2} = \frac{22 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} - \frac{\sqrt{22} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} - \frac{\sqrt{66} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{13}{3} + i \left(\frac{22 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}}\right)}}{9} - \frac{\sqrt{22} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6} + \frac{\sqrt{66} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{1407}}{173} \right)}}{3} \right)}}{6}\right)$$
               __________________                            
              /           ______                             
     13      /  173   I*\/ 1407                 22           
x3 = -- + 3 /   --- + ----------  + -------------------------
     3    \/     54       18               __________________
                                          /           ______ 
                                         /  173   I*\/ 1407  
                                    9*3 /   --- + ---------- 
                                      \/     54       18     
$$x_{3} = \frac{13}{3} + \frac{22}{9 \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}} + \sqrt[3]{\frac{173}{54} + \frac{\sqrt{1407} i}{18}}$$
x3 = 13/3 + 22/(9*(173/54 + sqrt(1407)*i/18)^(1/3)) + (173/54 + sqrt(1407)*i/18)^(1/3)
Respuesta numérica [src]
x1 = 7.40267882952119
x2 = 3.31603086087073
x3 = 2.28129030960809
x3 = 2.28129030960809