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1/(x-2)^2-1/x-2-6=0

1/(x-2)^2-1/x-2-6=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   1       1            
-------- - - - 2 - 6 = 0
       2   x            
(x - 2)                 
$$\left(\left(\frac{1}{\left(x - 2\right)^{2}} - \frac{1}{x}\right) - 2\right) - 6 = 0$$
Gráfica
Respuesta rápida [src]
                /                     1                      \     /        /                     1                      \                                                                      \                                                                      
          313*re|--------------------------------------------|     |  313*im|--------------------------------------------|              /    /     ________\\              /    /     ________\\|              /    /     ________\\              /    /     ________\\
                |                     _______________________|     |        |                     _______________________|              |    |12*\/ 112827 ||              |    |12*\/ 112827 |||              |    |12*\/ 112827 ||              |    |12*\/ 112827 ||
                |/          ___\     /              ________ |     |        |/          ___\     /              ________ |              |atan|-------------||              |atan|-------------|||              |atan|-------------||              |atan|-------------||
                ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     |        ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     _____    |    \     3797    /|     _____    |    \     3797    /||     _____    |    \     3797    /|     _____    |    \     3797    /|
                ||- - - -------|*3 /   ---- + -------------- |     |        ||- - - -------|*3 /   ---- + -------------- |   \/ 313 *sin|-------------------|   \/ 939 *cos|-------------------||   \/ 939 *sin|-------------------|   \/ 313 *cos|-------------------|
     31         \\  2      2   / \/    512         128       /     |        \\  2      2   / \/    512         128       /              \         3         /              \         3         /|              \         3         /              \         3         /
x1 = -- - ---------------------------------------------------- + I*|- ---------------------------------------------------- + -------------------------------- + --------------------------------| - -------------------------------- + --------------------------------
     24                           192                              \                          192                                           48                                 48               /                  48                                 48               
$$x_{1} = - \frac{\sqrt{939} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{\sqrt{313} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{31}{24} + i \left(- \frac{313 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{\sqrt{313} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{939} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48}\right)$$
                /                     1                      \     /        /                     1                      \                                                                      \                                                                      
          313*re|--------------------------------------------|     |  313*im|--------------------------------------------|              /    /     ________\\              /    /     ________\\|              /    /     ________\\              /    /     ________\\
                |                     _______________________|     |        |                     _______________________|              |    |12*\/ 112827 ||              |    |12*\/ 112827 |||              |    |12*\/ 112827 ||              |    |12*\/ 112827 ||
                |/          ___\     /              ________ |     |        |/          ___\     /              ________ |              |atan|-------------||              |atan|-------------|||              |atan|-------------||              |atan|-------------||
                ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     |        ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     _____    |    \     3797    /|     _____    |    \     3797    /||     _____    |    \     3797    /|     _____    |    \     3797    /|
                ||- - + -------|*3 /   ---- + -------------- |     |        ||- - + -------|*3 /   ---- + -------------- |   \/ 939 *cos|-------------------|   \/ 313 *sin|-------------------||   \/ 313 *cos|-------------------|   \/ 939 *sin|-------------------|
     31         \\  2      2   / \/    512         128       /     |        \\  2      2   / \/    512         128       /              \         3         /              \         3         /|              \         3         /              \         3         /
x2 = -- - ---------------------------------------------------- + I*|- ---------------------------------------------------- - -------------------------------- + --------------------------------| + -------------------------------- + --------------------------------
     24                           192                              \                          192                                           48                                 48               /                  48                                 48               
$$x_{2} = \frac{\sqrt{939} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{313} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{31}{24} + i \left(- \frac{\sqrt{939} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{313} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192}\right)$$
                                                  _______________________
                                                 /              ________ 
                                                /  3797   3*I*\/ 112827  
                                             3 /   ---- + -------------- 
     31                 313                  \/    512         128       
x3 = -- - -------------------------------- - ----------------------------
     24            _______________________                3              
                  /              ________                                
                 /  3797   3*I*\/ 112827                                 
          192*3 /   ---- + --------------                                
              \/    512         128                                      
$$x_{3} = \frac{31}{24} - \frac{\sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}{3} - \frac{313}{192 \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}$$
x3 = 31/24 - (3797/512 + 3*sqrt(112827)*i/128)^(1/3)/3 - 313/(192*(3797/512 + 3*sqrt(112827)*i/128)^(1/3))
Suma y producto de raíces [src]
suma
           /                     1                      \     /        /                     1                      \                                                                      \                                                                                    /                     1                      \     /        /                     1                      \                                                                      \                                                                                                                                             
     313*re|--------------------------------------------|     |  313*im|--------------------------------------------|              /    /     ________\\              /    /     ________\\|              /    /     ________\\              /    /     ________\\        313*re|--------------------------------------------|     |  313*im|--------------------------------------------|              /    /     ________\\              /    /     ________\\|              /    /     ________\\              /    /     ________\\                                                                       
           |                     _______________________|     |        |                     _______________________|              |    |12*\/ 112827 ||              |    |12*\/ 112827 |||              |    |12*\/ 112827 ||              |    |12*\/ 112827 ||              |                     _______________________|     |        |                     _______________________|              |    |12*\/ 112827 ||              |    |12*\/ 112827 |||              |    |12*\/ 112827 ||              |    |12*\/ 112827 ||                                                _______________________
           |/          ___\     /              ________ |     |        |/          ___\     /              ________ |              |atan|-------------||              |atan|-------------|||              |atan|-------------||              |atan|-------------||              |/          ___\     /              ________ |     |        |/          ___\     /              ________ |              |atan|-------------||              |atan|-------------|||              |atan|-------------||              |atan|-------------||                                               /              ________ 
           ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     |        ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     _____    |    \     3797    /|     _____    |    \     3797    /||     _____    |    \     3797    /|     _____    |    \     3797    /|              ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     |        ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     _____    |    \     3797    /|     _____    |    \     3797    /||     _____    |    \     3797    /|     _____    |    \     3797    /|                                              /  3797   3*I*\/ 112827  
           ||- - - -------|*3 /   ---- + -------------- |     |        ||- - - -------|*3 /   ---- + -------------- |   \/ 313 *sin|-------------------|   \/ 939 *cos|-------------------||   \/ 939 *sin|-------------------|   \/ 313 *cos|-------------------|              ||- - + -------|*3 /   ---- + -------------- |     |        ||- - + -------|*3 /   ---- + -------------- |   \/ 939 *cos|-------------------|   \/ 313 *sin|-------------------||   \/ 313 *cos|-------------------|   \/ 939 *sin|-------------------|                                           3 /   ---- + -------------- 
31         \\  2      2   / \/    512         128       /     |        \\  2      2   / \/    512         128       /              \         3         /              \         3         /|              \         3         /              \         3         /   31         \\  2      2   / \/    512         128       /     |        \\  2      2   / \/    512         128       /              \         3         /              \         3         /|              \         3         /              \         3         /   31                 313                  \/    512         128       
-- - ---------------------------------------------------- + I*|- ---------------------------------------------------- + -------------------------------- + --------------------------------| - -------------------------------- + -------------------------------- + -- - ---------------------------------------------------- + I*|- ---------------------------------------------------- - -------------------------------- + --------------------------------| + -------------------------------- + -------------------------------- + -- - -------------------------------- - ----------------------------
24                           192                              \                          192                                           48                                 48               /                  48                                 48                  24                           192                              \                          192                                           48                                 48               /                  48                                 48                  24            _______________________                3              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       /              ________                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      /  3797   3*I*\/ 112827                                 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               192*3 /   ---- + --------------                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \/    512         128                                      
$$\left(\left(\frac{\sqrt{939} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{313} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{31}{24} + i \left(- \frac{\sqrt{939} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{313} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192}\right)\right) + \left(- \frac{\sqrt{939} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{\sqrt{313} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{31}{24} + i \left(- \frac{313 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{\sqrt{313} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{939} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48}\right)\right)\right) + \left(\frac{31}{24} - \frac{\sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}{3} - \frac{313}{192 \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)$$
=
                                              /                     1                      \         /                     1                      \                                    /        /                     1                      \                                                                      \     /        /                     1                      \                                                                      \                                   
                                        313*re|--------------------------------------------|   313*re|--------------------------------------------|                                    |  313*im|--------------------------------------------|              /    /     ________\\              /    /     ________\\|     |  313*im|--------------------------------------------|              /    /     ________\\              /    /     ________\\|              /    /     ________\\
                                              |                     _______________________|         |                     _______________________|        _______________________     |        |                     _______________________|              |    |12*\/ 112827 ||              |    |12*\/ 112827 |||     |        |                     _______________________|              |    |12*\/ 112827 ||              |    |12*\/ 112827 |||              |    |12*\/ 112827 ||
                                              |/          ___\     /              ________ |         |/          ___\     /              ________ |       /              ________      |        |/          ___\     /              ________ |              |atan|-------------||              |atan|-------------|||     |        |/          ___\     /              ________ |              |atan|-------------||              |atan|-------------|||              |atan|-------------||
                                              ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |         ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |      /  3797   3*I*\/ 112827       |        ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     _____    |    \     3797    /|     _____    |    \     3797    /||     |        ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     _____    |    \     3797    /|     _____    |    \     3797    /||     _____    |    \     3797    /|
                                              ||- - + -------|*3 /   ---- + -------------- |         ||- - - -------|*3 /   ---- + -------------- |   3 /   ---- + --------------      |        ||- - + -------|*3 /   ---- + -------------- |   \/ 939 *cos|-------------------|   \/ 313 *sin|-------------------||     |        ||- - - -------|*3 /   ---- + -------------- |   \/ 313 *sin|-------------------|   \/ 939 *cos|-------------------||   \/ 313 *cos|-------------------|
31                 313                        \\  2      2   / \/    512         128       /         \\  2      2   / \/    512         128       /   \/    512         128            |        \\  2      2   / \/    512         128       /              \         3         /              \         3         /|     |        \\  2      2   / \/    512         128       /              \         3         /              \         3         /|              \         3         /
-- - -------------------------------- - ---------------------------------------------------- - ---------------------------------------------------- - ---------------------------- + I*|- ---------------------------------------------------- - -------------------------------- + --------------------------------| + I*|- ---------------------------------------------------- + -------------------------------- + --------------------------------| + --------------------------------
8             _______________________                           192                                                    192                                         3                   \                          192                                           48                                 48               /     \                          192                                           48                                 48               /                  24               
             /              ________                                                                                                                                                                                                                                                                                                                                                                                                                                                       
            /  3797   3*I*\/ 112827                                                                                                                                                                                                                                                                                                                                                                                                                                                        
     192*3 /   ---- + --------------                                                                                                                                                                                                                                                                                                                                                                                                                                                       
         \/    512         128                                                                                                                                                                                                                                                                                                                                                                                                                                                             
$$- \frac{313 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} - \frac{313 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{\sqrt{313} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{24} + \frac{31}{8} - \frac{\sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}{3} + i \left(- \frac{\sqrt{939} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{313} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192}\right) + i \left(- \frac{313 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{\sqrt{313} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{939} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48}\right) - \frac{313}{192 \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}$$
producto
/           /                     1                      \     /        /                     1                      \                                                                      \                                                                      \ /           /                     1                      \     /        /                     1                      \                                                                      \                                                                      \                                                                       
|     313*re|--------------------------------------------|     |  313*im|--------------------------------------------|              /    /     ________\\              /    /     ________\\|              /    /     ________\\              /    /     ________\\| |     313*re|--------------------------------------------|     |  313*im|--------------------------------------------|              /    /     ________\\              /    /     ________\\|              /    /     ________\\              /    /     ________\\|                                                                       
|           |                     _______________________|     |        |                     _______________________|              |    |12*\/ 112827 ||              |    |12*\/ 112827 |||              |    |12*\/ 112827 ||              |    |12*\/ 112827 ||| |           |                     _______________________|     |        |                     _______________________|              |    |12*\/ 112827 ||              |    |12*\/ 112827 |||              |    |12*\/ 112827 ||              |    |12*\/ 112827 ||| /                                             _______________________\
|           |/          ___\     /              ________ |     |        |/          ___\     /              ________ |              |atan|-------------||              |atan|-------------|||              |atan|-------------||              |atan|-------------||| |           |/          ___\     /              ________ |     |        |/          ___\     /              ________ |              |atan|-------------||              |atan|-------------|||              |atan|-------------||              |atan|-------------||| |                                            /              ________ |
|           ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     |        ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     _____    |    \     3797    /|     _____    |    \     3797    /||     _____    |    \     3797    /|     _____    |    \     3797    /|| |           ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     |        ||  1   I*\/ 3 |    /  3797   3*I*\/ 112827  |     _____    |    \     3797    /|     _____    |    \     3797    /||     _____    |    \     3797    /|     _____    |    \     3797    /|| |                                           /  3797   3*I*\/ 112827  |
|           ||- - - -------|*3 /   ---- + -------------- |     |        ||- - - -------|*3 /   ---- + -------------- |   \/ 313 *sin|-------------------|   \/ 939 *cos|-------------------||   \/ 939 *sin|-------------------|   \/ 313 *cos|-------------------|| |           ||- - + -------|*3 /   ---- + -------------- |     |        ||- - + -------|*3 /   ---- + -------------- |   \/ 939 *cos|-------------------|   \/ 313 *sin|-------------------||   \/ 313 *cos|-------------------|   \/ 939 *sin|-------------------|| |                                        3 /   ---- + -------------- |
|31         \\  2      2   / \/    512         128       /     |        \\  2      2   / \/    512         128       /              \         3         /              \         3         /|              \         3         /              \         3         /| |31         \\  2      2   / \/    512         128       /     |        \\  2      2   / \/    512         128       /              \         3         /              \         3         /|              \         3         /              \         3         /| |31                 313                  \/    512         128       |
|-- - ---------------------------------------------------- + I*|- ---------------------------------------------------- + -------------------------------- + --------------------------------| - -------------------------------- + --------------------------------|*|-- - ---------------------------------------------------- + I*|- ---------------------------------------------------- - -------------------------------- + --------------------------------| + -------------------------------- + --------------------------------|*|-- - -------------------------------- - ----------------------------|
\24                           192                              \                          192                                           48                                 48               /                  48                                 48               / \24                           192                              \                          192                                           48                                 48               /                  48                                 48               / |24            _______________________                3              |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |             /              ________                                |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |            /  3797   3*I*\/ 112827                                 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |     192*3 /   ---- + --------------                                |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          \         \/    512         128                                      /
$$\left(- \frac{\sqrt{939} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{\sqrt{313} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{31}{24} + i \left(- \frac{313 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{\sqrt{313} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{939} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48}\right)\right) \left(\frac{\sqrt{939} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{313} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192} + \frac{31}{24} + i \left(- \frac{\sqrt{939} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} + \frac{\sqrt{313} \sin{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}}{48} - \frac{313 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)}}{192}\right)\right) \left(\frac{31}{24} - \frac{\sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}{3} - \frac{313}{192 \sqrt[3]{\frac{3797}{512} + \frac{3 \sqrt{112827} i}{128}}}\right)$$
=
                                                                        /             /      /     ________\\                 /    /     ________\\\ 
                                                                        |             |      |12*\/ 112827 ||                 |    |12*\/ 112827 ||| 
 /         ________________________ /        ________________________\\ |             |2*atan|-------------||                 |atan|-------------||| 
 |      3 /               ________  |     3 /               ________ || |             |      \     3797    /|        _____    |    \     3797    /|| 
-\313 - \/  3797 + 12*I*\/ 112827  *\31 - \/  3797 + 12*I*\/ 112827  //*|648 + 626*cos|---------------------| + 62*\/ 313 *cos|-------------------|| 
                                                                        \             \          3          /                 \         3         // 
-----------------------------------------------------------------------------------------------------------------------------------------------------
                                                                   ________________________                                                          
                                                                3 /               ________                                                           
                                                          13824*\/  3797 + 12*I*\/ 112827                                                            
$$- \frac{\left(313 - \left(31 - \sqrt[3]{3797 + 12 \sqrt{112827} i}\right) \sqrt[3]{3797 + 12 \sqrt{112827} i}\right) \left(626 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)} + 648 + 62 \sqrt{313} \cos{\left(\frac{\operatorname{atan}{\left(\frac{12 \sqrt{112827}}{3797} \right)}}{3} \right)}\right)}{13824 \sqrt[3]{3797 + 12 \sqrt{112827} i}}$$
-(313 - (3797 + 12*i*sqrt(112827))^(1/3)*(31 - (3797 + 12*i*sqrt(112827))^(1/3)))*(648 + 626*cos(2*atan(12*sqrt(112827)/3797)/3) + 62*sqrt(313)*cos(atan(12*sqrt(112827)/3797)/3))/(13824*(3797 + 12*i*sqrt(112827))^(1/3))
Respuesta numérica [src]
x1 = 1.65905737491939 + 0.e-20*i
x2 = 2.34448915873198 - 0.e-23*i
x3 = -0.128546533651372 + 0.e-21*i
x3 = -0.128546533651372 + 0.e-21*i
Gráfico
1/(x-2)^2-1/x-2-6=0 la ecuación