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(1-x^3)/(4*x^2-3*x-10)=1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
          3        
     1 - x         
--------------- = 1
   2               
4*x  - 3*x - 10    
$$\frac{1 - x^{3}}{\left(4 x^{2} - 3 x\right) - 10} = 1$$
Gráfica
Suma y producto de raíces [src]
suma
                                     /                  1                   \     /                                 /                  1                   \                                \                                                                        /                  1                   \     /                                 /                  1                   \                                \                                                                                          
           /    /    ______\\   25*re|--------------------------------------|     |       /    /    ______\\   25*im|--------------------------------------|              /    /    ______\\|              /    /    ______\\              /    /    ______\\   25*re|--------------------------------------|     |       /    /    ______\\   25*im|--------------------------------------|              /    /    ______\\|              /    /    ______\\                                                          
           |    |3*\/ 6531 ||        |                     _________________|     |       |    |3*\/ 6531 ||        |                     _________________|              |    |3*\/ 6531 |||              |    |3*\/ 6531 ||              |    |3*\/ 6531 ||        |                     _________________|     |       |    |3*\/ 6531 ||        |                     _________________|              |    |3*\/ 6531 |||              |    |3*\/ 6531 ||                                                          
           |atan|----------||        |/          ___\     /          ______ |     |       |atan|----------||        |/          ___\     /          ______ |              |atan|----------|||              |atan|----------||              |atan|----------||        |/          ___\     /          ______ |     |       |atan|----------||        |/          ___\     /          ______ |              |atan|----------|||              |atan|----------||                                                          
           |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |     |       |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |       ___    |    \    61    /||       ___    |    \    61    /|              |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |     |       |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |       ___    |    \    61    /||       ___    |    \    61    /|              _________________                           
      5*cos|----------------|        ||- - - -------|*3 /   -- + ---------- |     |  5*sin|----------------|        ||- - - -------|*3 /   -- + ---------- |   5*\/ 3 *cos|----------------||   5*\/ 3 *sin|----------------|         5*cos|----------------|        ||- - + -------|*3 /   -- + ---------- |     |  5*sin|----------------|        ||- - + -------|*3 /   -- + ---------- |   5*\/ 3 *cos|----------------||   5*\/ 3 *sin|----------------|             /          ______                            
  4        \       3        /        \\  2      2   / \/    54       18     /     |       \       3        /        \\  2      2   / \/    54       18     /              \       3        /|              \       3        /     4        \       3        /        \\  2      2   / \/    54       18     /     |       \       3        /        \\  2      2   / \/    54       18     /              \       3        /|              \       3        /     4      /  61   I*\/ 6531                25           
- - - ----------------------- + --------------------------------------------- + I*|- ----------------------- + --------------------------------------------- - -----------------------------| + ----------------------------- + - - - ----------------------- + --------------------------------------------- + I*|- ----------------------- + --------------------------------------------- + -----------------------------| - ----------------------------- + - - + 3 /   -- + ----------  + ------------------------
  3              6                                    9                           \             6                                    9                                       6              /                 6                   3              6                                    9                           \             6                                    9                                       6              /                 6                   3   \/    54       18               _________________
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     /          ______ 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /  61   I*\/ 6531  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               9*3 /   -- + ---------- 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 \/    54       18     
$$\left(- \frac{4}{3} + \frac{25}{9 \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}} + \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}\right) + \left(\left(\frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} - \frac{4}{3} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} - \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + i \left(\frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6}\right)\right) + \left(- \frac{4}{3} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} + \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9}\right)\right)\right)$$
=
                                                                                        /                  1                   \        /                  1                   \     /                                 /                  1                   \                                \     /                                 /                  1                   \                                \
                                   /    /    ______\\                              25*re|--------------------------------------|   25*re|--------------------------------------|     |       /    /    ______\\   25*im|--------------------------------------|              /    /    ______\\|     |       /    /    ______\\   25*im|--------------------------------------|              /    /    ______\\|
                                   |    |3*\/ 6531 ||                                   |                     _________________|        |                     _________________|     |       |    |3*\/ 6531 ||        |                     _________________|              |    |3*\/ 6531 |||     |       |    |3*\/ 6531 ||        |                     _________________|              |    |3*\/ 6531 |||
                                   |atan|----------||                                   |/          ___\     /          ______ |        |/          ___\     /          ______ |     |       |atan|----------||        |/          ___\     /          ______ |              |atan|----------|||     |       |atan|----------||        |/          ___\     /          ______ |              |atan|----------|||
          _________________        |    \    61    /|                                   ||  1   I*\/ 3 |    /  61   I*\/ 6531  |        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |     |       |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |       ___    |    \    61    /||     |       |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |       ___    |    \    61    /||
         /          ______    5*cos|----------------|                                   ||- - + -------|*3 /   -- + ---------- |        ||- - - -------|*3 /   -- + ---------- |     |  5*sin|----------------|        ||- - + -------|*3 /   -- + ---------- |   5*\/ 3 *cos|----------------||     |  5*sin|----------------|        ||- - - -------|*3 /   -- + ---------- |   5*\/ 3 *cos|----------------||
        /  61   I*\/ 6531          \       3        /              25                   \\  2      2   / \/    54       18     /        \\  2      2   / \/    54       18     /     |       \       3        /        \\  2      2   / \/    54       18     /              \       3        /|     |       \       3        /        \\  2      2   / \/    54       18     /              \       3        /|
-4 + 3 /   -- + ----------  - ----------------------- + ------------------------ + --------------------------------------------- + --------------------------------------------- + I*|- ----------------------- + --------------------------------------------- + -----------------------------| + I*|- ----------------------- + --------------------------------------------- - -----------------------------|
     \/    54       18                   3                     _________________                         9                                               9                           \             6                                    9                                       6              /     \             6                                    9                                       6              /
                                                              /          ______                                                                                                                                                                                                                                                                                                                                 
                                                             /  61   I*\/ 6531                                                                                                                                                                                                                                                                                                                                  
                                                        9*3 /   -- + ----------                                                                                                                                                                                                                                                                                                                                 
                                                          \/    54       18                                                                                                                                                                                                                                                                                                                                     
$$-4 - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{3} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} + \frac{25}{9 \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}} + i \left(\frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6}\right) + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9}\right) + \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}$$
producto
/                                     /                  1                   \     /                                 /                  1                   \                                \                                \ /                                     /                  1                   \     /                                 /                  1                   \                                \                                \                                                          
|           /    /    ______\\   25*re|--------------------------------------|     |       /    /    ______\\   25*im|--------------------------------------|              /    /    ______\\|              /    /    ______\\| |           /    /    ______\\   25*re|--------------------------------------|     |       /    /    ______\\   25*im|--------------------------------------|              /    /    ______\\|              /    /    ______\\|                                                          
|           |    |3*\/ 6531 ||        |                     _________________|     |       |    |3*\/ 6531 ||        |                     _________________|              |    |3*\/ 6531 |||              |    |3*\/ 6531 ||| |           |    |3*\/ 6531 ||        |                     _________________|     |       |    |3*\/ 6531 ||        |                     _________________|              |    |3*\/ 6531 |||              |    |3*\/ 6531 |||                                                          
|           |atan|----------||        |/          ___\     /          ______ |     |       |atan|----------||        |/          ___\     /          ______ |              |atan|----------|||              |atan|----------||| |           |atan|----------||        |/          ___\     /          ______ |     |       |atan|----------||        |/          ___\     /          ______ |              |atan|----------|||              |atan|----------|||                                                          
|           |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |     |       |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |       ___    |    \    61    /||       ___    |    \    61    /|| |           |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |     |       |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |       ___    |    \    61    /||       ___    |    \    61    /|| /           _________________                           \
|      5*cos|----------------|        ||- - - -------|*3 /   -- + ---------- |     |  5*sin|----------------|        ||- - - -------|*3 /   -- + ---------- |   5*\/ 3 *cos|----------------||   5*\/ 3 *sin|----------------|| |      5*cos|----------------|        ||- - + -------|*3 /   -- + ---------- |     |  5*sin|----------------|        ||- - + -------|*3 /   -- + ---------- |   5*\/ 3 *cos|----------------||   5*\/ 3 *sin|----------------|| |          /          ______                            |
|  4        \       3        /        \\  2      2   / \/    54       18     /     |       \       3        /        \\  2      2   / \/    54       18     /              \       3        /|              \       3        /| |  4        \       3        /        \\  2      2   / \/    54       18     /     |       \       3        /        \\  2      2   / \/    54       18     /              \       3        /|              \       3        /| |  4      /  61   I*\/ 6531                25           |
|- - - ----------------------- + --------------------------------------------- + I*|- ----------------------- + --------------------------------------------- - -----------------------------| + -----------------------------|*|- - - ----------------------- + --------------------------------------------- + I*|- ----------------------- + --------------------------------------------- + -----------------------------| - -----------------------------|*|- - + 3 /   -- + ----------  + ------------------------|
\  3              6                                    9                           \             6                                    9                                       6              /                 6              / \  3              6                                    9                           \             6                                    9                                       6              /                 6              / |  3   \/    54       18               _________________|
                                                                                                                                                                                                                                                                                                                                                                                                                                                                |                                     /          ______ |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                |                                    /  61   I*\/ 6531  |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                |                               9*3 /   -- + ---------- |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                \                                 \/    54       18     /
$$\left(- \frac{4}{3} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} + \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9}\right)\right) \left(\frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} - \frac{4}{3} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} - \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + i \left(\frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6}\right)\right) \left(- \frac{4}{3} + \frac{25}{9 \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}} + \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}\right)$$
=
                                                                       /             /    /    ______\\          /      /    ______\\\
                                                                       |             |    |3*\/ 6531 ||          |      |3*\/ 6531 |||
/              ___________________ /             ___________________\\ |             |atan|----------||          |2*atan|----------|||
|   3 ___   3 /            ______  |      2/3 3 /            ______ || |             |    \    61    /|          |      \    61    /||
\50*\/ 2  + \/  61 + 3*I*\/ 6531  *\-8 + 2   *\/  61 + 3*I*\/ 6531  //*|-36 + 160*cos|----------------| + 200*cos|------------------||
                                                                       \             \       3        /          \        3         //
--------------------------------------------------------------------------------------------------------------------------------------
                                                             ___________________                                                      
                                                          3 /            ______                                                       
                                                      216*\/  61 + 3*I*\/ 6531                                                        
$$\frac{\left(50 \sqrt[3]{2} + \left(-8 + 2^{\frac{2}{3}} \sqrt[3]{61 + 3 \sqrt{6531} i}\right) \sqrt[3]{61 + 3 \sqrt{6531} i}\right) \left(-36 + 200 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)} + 160 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}\right)}{216 \sqrt[3]{61 + 3 \sqrt{6531} i}}$$
(50*2^(1/3) + (61 + 3*i*sqrt(6531))^(1/3)*(-8 + 2^(2/3)*(61 + 3*i*sqrt(6531))^(1/3)))*(-36 + 160*cos(atan(3*sqrt(6531)/61)/3) + 200*cos(2*atan(3*sqrt(6531)/61)/3))/(216*(61 + 3*i*sqrt(6531))^(1/3))
Respuesta rápida [src]
                                          /                  1                   \     /                                 /                  1                   \                                \                                
                /    /    ______\\   25*re|--------------------------------------|     |       /    /    ______\\   25*im|--------------------------------------|              /    /    ______\\|              /    /    ______\\
                |    |3*\/ 6531 ||        |                     _________________|     |       |    |3*\/ 6531 ||        |                     _________________|              |    |3*\/ 6531 |||              |    |3*\/ 6531 ||
                |atan|----------||        |/          ___\     /          ______ |     |       |atan|----------||        |/          ___\     /          ______ |              |atan|----------|||              |atan|----------||
                |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |     |       |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |       ___    |    \    61    /||       ___    |    \    61    /|
           5*cos|----------------|        ||- - - -------|*3 /   -- + ---------- |     |  5*sin|----------------|        ||- - - -------|*3 /   -- + ---------- |   5*\/ 3 *cos|----------------||   5*\/ 3 *sin|----------------|
       4        \       3        /        \\  2      2   / \/    54       18     /     |       \       3        /        \\  2      2   / \/    54       18     /              \       3        /|              \       3        /
x1 = - - - ----------------------- + --------------------------------------------- + I*|- ----------------------- + --------------------------------------------- - -----------------------------| + -----------------------------
       3              6                                    9                           \             6                                    9                                       6              /                 6              
$$x_{1} = - \frac{4}{3} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} + \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + i \left(- \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9}\right)$$
                                          /                  1                   \     /                                 /                  1                   \                                \                                
                /    /    ______\\   25*re|--------------------------------------|     |       /    /    ______\\   25*im|--------------------------------------|              /    /    ______\\|              /    /    ______\\
                |    |3*\/ 6531 ||        |                     _________________|     |       |    |3*\/ 6531 ||        |                     _________________|              |    |3*\/ 6531 |||              |    |3*\/ 6531 ||
                |atan|----------||        |/          ___\     /          ______ |     |       |atan|----------||        |/          ___\     /          ______ |              |atan|----------|||              |atan|----------||
                |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |     |       |    \    61    /|        ||  1   I*\/ 3 |    /  61   I*\/ 6531  |       ___    |    \    61    /||       ___    |    \    61    /|
           5*cos|----------------|        ||- - + -------|*3 /   -- + ---------- |     |  5*sin|----------------|        ||- - + -------|*3 /   -- + ---------- |   5*\/ 3 *cos|----------------||   5*\/ 3 *sin|----------------|
       4        \       3        /        \\  2      2   / \/    54       18     /     |       \       3        /        \\  2      2   / \/    54       18     /              \       3        /|              \       3        /
x2 = - - - ----------------------- + --------------------------------------------- + I*|- ----------------------- + --------------------------------------------- + -----------------------------| - -----------------------------
       3              6                                    9                           \             6                                    9                                       6              /                 6              
$$x_{2} = \frac{25 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} - \frac{4}{3} - \frac{5 \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} - \frac{5 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + i \left(\frac{25 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}}\right)}}{9} - \frac{5 \sin{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6} + \frac{5 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{3 \sqrt{6531}}{61} \right)}}{3} \right)}}{6}\right)$$
                _________________                           
               /          ______                            
       4      /  61   I*\/ 6531                25           
x3 = - - + 3 /   -- + ----------  + ------------------------
       3   \/    54       18               _________________
                                          /          ______ 
                                         /  61   I*\/ 6531  
                                    9*3 /   -- + ---------- 
                                      \/    54       18     
$$x_{3} = - \frac{4}{3} + \frac{25}{9 \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}} + \sqrt[3]{\frac{61}{54} + \frac{\sqrt{6531} i}{18}}$$
x3 = -4/3 + 25/(9*(61/54 + sqrt(6531)*i/18)^(1/3)) + (61/54 + sqrt(6531)*i/18)^(1/3)
Respuesta numérica [src]
x1 = -1.6069012845906 - 0.e-22*i
x2 = -4.07356235130883 + 0.e-22*i
x3 = 1.68046363589943 - 0.e-20*i
x3 = 1.68046363589943 - 0.e-20*i