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2*x^-2-2*x-13/2=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
2          13    
-- - 2*x - -- = 0
 2         2     
x                
$$\left(- 2 x + \frac{2}{x^{2}}\right) - \frac{13}{2} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
             /                    1                     \                                 /        /                    1                     \                                                              \                                                  /                    1                     \                                 /        /                    1                     \                                                              \                                                                                                      
       169*re|------------------------------------------|         /    /     ______\\     |  169*im|------------------------------------------|         /    /     ______\\               /    /     ______\\|               /    /     ______\\          169*re|------------------------------------------|         /    /     ______\\     |  169*im|------------------------------------------|         /    /     ______\\               /    /     ______\\|               /    /     ______\\                                                                    
             |                     _____________________|         |    |24*\/ 5295 ||     |        |                     _____________________|         |    |24*\/ 5295 ||               |    |24*\/ 5295 |||               |    |24*\/ 5295 ||                |                     _____________________|         |    |24*\/ 5295 ||     |        |                     _____________________|         |    |24*\/ 5295 ||               |    |24*\/ 5295 |||               |    |24*\/ 5295 ||                                               _____________________
             |/          ___\     /              ______ |         |atan|-----------||     |        |/          ___\     /              ______ |         |atan|-----------||               |atan|-----------|||               |atan|-----------||                |/          ___\     /              ______ |         |atan|-----------||     |        |/          ___\     /              ______ |         |atan|-----------||               |atan|-----------|||               |atan|-----------||                                              /              ______ 
             ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|     |        ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|        ___    |    \    1333   /||        ___    |    \    1333   /|                ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|     |        ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|        ___    |    \    1333   /||        ___    |    \    1333   /|                                             /  1333   3*I*\/ 5295  
             ||- - - -------|*3 /   ---- + ------------ |   13*cos|-----------------|     |        ||- - - -------|*3 /   ---- + ------------ |   13*sin|-----------------|   13*\/ 3 *cos|-----------------||   13*\/ 3 *sin|-----------------|                ||- - + -------|*3 /   ---- + ------------ |   13*cos|-----------------|     |        ||- - + -------|*3 /   ---- + ------------ |   13*sin|-----------------|   13*\/ 3 *cos|-----------------||   13*\/ 3 *sin|-----------------|                                          3 /   ---- + ------------ 
  13         \\  2      2   / \/     64         8       /         \        3        /     |        \\  2      2   / \/     64         8       /         \        3        /               \        3        /|               \        3        /     13         \\  2      2   / \/     64         8       /         \        3        /     |        \\  2      2   / \/     64         8       /         \        3        /               \        3        /|               \        3        /     13                169                \/     64         8       
- -- - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- + -------------------------------| - ------------------------------- + - -- - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- - -------------------------------| + ------------------------------- + - -- - ----------------------------- - --------------------------
  12                           48                                       24                \                          48                                       24                             24              /                  24                   12                           48                                       24                \                          48                                       24                             24              /                  24                   12           _____________________               3             
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /              ______                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /  1333   3*I*\/ 5295                               
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             48*3 /   ---- + ------------                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \/     64         8                                    
$$\left(\left(- \frac{13}{12} + \frac{13 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + i \left(- \frac{13 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48}\right)\right) + \left(- \frac{13}{12} - \frac{13 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + \frac{13 \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + i \left(- \frac{169 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + \frac{13 \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24}\right)\right)\right) + \left(- \frac{13}{12} - \frac{\sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}{3} - \frac{169}{48 \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)$$
=
                                             /                    1                     \         /                    1                     \                                                              /        /                    1                     \                                                              \     /        /                    1                     \                                                              \
                                       169*re|------------------------------------------|   169*re|------------------------------------------|                                      /    /     ______\\     |  169*im|------------------------------------------|         /    /     ______\\               /    /     ______\\|     |  169*im|------------------------------------------|         /    /     ______\\               /    /     ______\\|
                                             |                     _____________________|         |                     _____________________|        _____________________         |    |24*\/ 5295 ||     |        |                     _____________________|         |    |24*\/ 5295 ||               |    |24*\/ 5295 |||     |        |                     _____________________|         |    |24*\/ 5295 ||               |    |24*\/ 5295 |||
                                             |/          ___\     /              ______ |         |/          ___\     /              ______ |       /              ______          |atan|-----------||     |        |/          ___\     /              ______ |         |atan|-----------||               |atan|-----------|||     |        |/          ___\     /              ______ |         |atan|-----------||               |atan|-----------|||
                                             ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |      /  1333   3*I*\/ 5295           |    \    1333   /|     |        ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|        ___    |    \    1333   /||     |        ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|        ___    |    \    1333   /||
                                             ||- - + -------|*3 /   ---- + ------------ |         ||- - - -------|*3 /   ---- + ------------ |   3 /   ---- + ------------    13*cos|-----------------|     |        ||- - + -------|*3 /   ---- + ------------ |   13*sin|-----------------|   13*\/ 3 *cos|-----------------||     |        ||- - - -------|*3 /   ---- + ------------ |   13*sin|-----------------|   13*\/ 3 *cos|-----------------||
  13                169                      \\  2      2   / \/     64         8       /         \\  2      2   / \/     64         8       /   \/     64         8                \        3        /     |        \\  2      2   / \/     64         8       /         \        3        /               \        3        /|     |        \\  2      2   / \/     64         8       /         \        3        /               \        3        /|
- -- - ----------------------------- - -------------------------------------------------- - -------------------------------------------------- - -------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- - -------------------------------| + I*|- -------------------------------------------------- + ------------------------- + -------------------------------|
  4            _____________________                           48                                                   48                                       3                            12                \                          48                                       24                             24              /     \                          48                                       24                             24              /
              /              ______                                                                                                                                                                                                                                                                                                                                                                                                                      
             /  1333   3*I*\/ 5295                                                                                                                                                                                                                                                                                                                                                                                                                       
       48*3 /   ---- + ------------                                                                                                                                                                                                                                                                                                                                                                                                                      
          \/     64         8                                                                                                                                                                                                                                                                                                                                                                                                                            
$$- \frac{13}{4} - \frac{169 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} - \frac{169 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + \frac{13 \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{12} - \frac{\sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}{3} + i \left(- \frac{169 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + \frac{13 \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24}\right) + i \left(- \frac{13 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48}\right) - \frac{169}{48 \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}$$
producto
/             /                    1                     \                                 /        /                    1                     \                                                              \                                  \ /             /                    1                     \                                 /        /                    1                     \                                                              \                                  \                                                                    
|       169*re|------------------------------------------|         /    /     ______\\     |  169*im|------------------------------------------|         /    /     ______\\               /    /     ______\\|               /    /     ______\\| |       169*re|------------------------------------------|         /    /     ______\\     |  169*im|------------------------------------------|         /    /     ______\\               /    /     ______\\|               /    /     ______\\|                                                                    
|             |                     _____________________|         |    |24*\/ 5295 ||     |        |                     _____________________|         |    |24*\/ 5295 ||               |    |24*\/ 5295 |||               |    |24*\/ 5295 ||| |             |                     _____________________|         |    |24*\/ 5295 ||     |        |                     _____________________|         |    |24*\/ 5295 ||               |    |24*\/ 5295 |||               |    |24*\/ 5295 ||| /                                            _____________________\
|             |/          ___\     /              ______ |         |atan|-----------||     |        |/          ___\     /              ______ |         |atan|-----------||               |atan|-----------|||               |atan|-----------||| |             |/          ___\     /              ______ |         |atan|-----------||     |        |/          ___\     /              ______ |         |atan|-----------||               |atan|-----------|||               |atan|-----------||| |                                           /              ______ |
|             ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|     |        ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|        ___    |    \    1333   /||        ___    |    \    1333   /|| |             ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|     |        ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|        ___    |    \    1333   /||        ___    |    \    1333   /|| |                                          /  1333   3*I*\/ 5295  |
|             ||- - - -------|*3 /   ---- + ------------ |   13*cos|-----------------|     |        ||- - - -------|*3 /   ---- + ------------ |   13*sin|-----------------|   13*\/ 3 *cos|-----------------||   13*\/ 3 *sin|-----------------|| |             ||- - + -------|*3 /   ---- + ------------ |   13*cos|-----------------|     |        ||- - + -------|*3 /   ---- + ------------ |   13*sin|-----------------|   13*\/ 3 *cos|-----------------||   13*\/ 3 *sin|-----------------|| |                                       3 /   ---- + ------------ |
|  13         \\  2      2   / \/     64         8       /         \        3        /     |        \\  2      2   / \/     64         8       /         \        3        /               \        3        /|               \        3        /| |  13         \\  2      2   / \/     64         8       /         \        3        /     |        \\  2      2   / \/     64         8       /         \        3        /               \        3        /|               \        3        /| |  13                169                \/     64         8       |
|- -- - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- + -------------------------------| - -------------------------------|*|- -- - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- - -------------------------------| + -------------------------------|*|- -- - ----------------------------- - --------------------------|
\  12                           48                                       24                \                          48                                       24                             24              /                  24              / \  12                           48                                       24                \                          48                                       24                             24              /                  24              / |  12           _____________________               3             |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |              /              ______                              |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |             /  1333   3*I*\/ 5295                               |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |       48*3 /   ---- + ------------                              |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \          \/     64         8                                    /
$$\left(- \frac{13}{12} - \frac{13 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + \frac{13 \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + i \left(- \frac{169 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + \frac{13 \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24}\right)\right) \left(- \frac{13}{12} + \frac{13 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + i \left(- \frac{13 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48}\right)\right) \left(- \frac{13}{12} - \frac{\sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}{3} - \frac{169}{48 \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)$$
=
                                                                       /     /      /     ______\\      /    /     ______\\\
                                                                       |     |      |24*\/ 5295 ||      |    |24*\/ 5295 |||
    /         ______________________ /        ______________________\\ |     |2*atan|-----------||      |atan|-----------|||
    |      3 /               ______  |     3 /               ______ || |     |      \    1333   /|      |    \    1333   /||
169*\169 + \/  1333 + 24*I*\/ 5295  *\13 + \/  1333 + 24*I*\/ 5295  //*|- cos|-------------------| + cos|-----------------||
                                                                       \     \         3         /      \        3        //
----------------------------------------------------------------------------------------------------------------------------
                                                      ______________________                                                
                                                   3 /               ______                                                 
                                               864*\/  1333 + 24*I*\/ 5295                                                  
$$\frac{169 \left(169 + \left(13 + \sqrt[3]{1333 + 24 \sqrt{5295} i}\right) \sqrt[3]{1333 + 24 \sqrt{5295} i}\right) \left(- \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)} + \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}\right)}{864 \sqrt[3]{1333 + 24 \sqrt{5295} i}}$$
169*(169 + (1333 + 24*i*sqrt(5295))^(1/3)*(13 + (1333 + 24*i*sqrt(5295))^(1/3)))*(-cos(2*atan(24*sqrt(5295)/1333)/3) + cos(atan(24*sqrt(5295)/1333)/3))/(864*(1333 + 24*i*sqrt(5295))^(1/3))
Respuesta rápida [src]
                  /                    1                     \                                 /        /                    1                     \                                                              \                                  
            169*re|------------------------------------------|         /    /     ______\\     |  169*im|------------------------------------------|         /    /     ______\\               /    /     ______\\|               /    /     ______\\
                  |                     _____________________|         |    |24*\/ 5295 ||     |        |                     _____________________|         |    |24*\/ 5295 ||               |    |24*\/ 5295 |||               |    |24*\/ 5295 ||
                  |/          ___\     /              ______ |         |atan|-----------||     |        |/          ___\     /              ______ |         |atan|-----------||               |atan|-----------|||               |atan|-----------||
                  ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|     |        ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|        ___    |    \    1333   /||        ___    |    \    1333   /|
                  ||- - - -------|*3 /   ---- + ------------ |   13*cos|-----------------|     |        ||- - - -------|*3 /   ---- + ------------ |   13*sin|-----------------|   13*\/ 3 *cos|-----------------||   13*\/ 3 *sin|-----------------|
       13         \\  2      2   / \/     64         8       /         \        3        /     |        \\  2      2   / \/     64         8       /         \        3        /               \        3        /|               \        3        /
x1 = - -- - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- + -------------------------------| - -------------------------------
       12                           48                                       24                \                          48                                       24                             24              /                  24              
$$x_{1} = - \frac{13}{12} - \frac{13 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + \frac{13 \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + i \left(- \frac{169 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + \frac{13 \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24}\right)$$
                  /                    1                     \                                 /        /                    1                     \                                                              \                                  
            169*re|------------------------------------------|         /    /     ______\\     |  169*im|------------------------------------------|         /    /     ______\\               /    /     ______\\|               /    /     ______\\
                  |                     _____________________|         |    |24*\/ 5295 ||     |        |                     _____________________|         |    |24*\/ 5295 ||               |    |24*\/ 5295 |||               |    |24*\/ 5295 ||
                  |/          ___\     /              ______ |         |atan|-----------||     |        |/          ___\     /              ______ |         |atan|-----------||               |atan|-----------|||               |atan|-----------||
                  ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|     |        ||  1   I*\/ 3 |    /  1333   3*I*\/ 5295  |         |    \    1333   /|        ___    |    \    1333   /||        ___    |    \    1333   /|
                  ||- - + -------|*3 /   ---- + ------------ |   13*cos|-----------------|     |        ||- - + -------|*3 /   ---- + ------------ |   13*sin|-----------------|   13*\/ 3 *cos|-----------------||   13*\/ 3 *sin|-----------------|
       13         \\  2      2   / \/     64         8       /         \        3        /     |        \\  2      2   / \/     64         8       /         \        3        /               \        3        /|               \        3        /
x2 = - -- - -------------------------------------------------- + ------------------------- + I*|- -------------------------------------------------- + ------------------------- - -------------------------------| + -------------------------------
       12                           48                                       24                \                          48                                       24                             24              /                  24              
$$x_{2} = - \frac{13}{12} + \frac{13 \sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48} + i \left(- \frac{13 \sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} + \frac{13 \sin{\left(\frac{\operatorname{atan}{\left(\frac{24 \sqrt{5295}}{1333} \right)}}{3} \right)}}{24} - \frac{169 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}\right)}}{48}\right)$$
                                                 _____________________
                                                /              ______ 
                                               /  1333   3*I*\/ 5295  
                                            3 /   ---- + ------------ 
       13                169                \/     64         8       
x3 = - -- - ----------------------------- - --------------------------
       12           _____________________               3             
                   /              ______                              
                  /  1333   3*I*\/ 5295                               
            48*3 /   ---- + ------------                              
               \/     64         8                                    
$$x_{3} = - \frac{13}{12} - \frac{\sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}{3} - \frac{169}{48 \sqrt[3]{\frac{1333}{64} + \frac{3 \sqrt{5295} i}{8}}}$$
x3 = -13/12 - (1333/64 + 3*sqrt(5295)*i/8)^(1/3)/3 - 169/(48*(1333/64 + 3*sqrt(5295)*i/8)^(1/3))
Respuesta numérica [src]
x1 = -0.616178966141236 + 0.e-22*i
x2 = 0.51534449568304 - 0.e-22*i
x3 = -3.1491655295418 + 0.e-23*i
x3 = -3.1491655295418 + 0.e-23*i