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x*(x^2-1)-1*3/20=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución numérica:

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Solución

Ha introducido [src]
  / 2    \   3     
x*\x  - 1/ - -- = 0
             20    
x(x21)320=0x \left(x^{2} - 1\right) - \frac{3}{20} = 0
Gráfica
05-15-10-51015-25002500
Respuesta rápida [src]
                             /                  1                   \     /                          /                  1                   \                            \                            
        /    /  ______\\   re|--------------------------------------|     |     /    /  ______\\   im|--------------------------------------|            /    /  ______\\|            /    /  ______\\
        |    |\/ 4071 ||     |                     _________________|     |     |    |\/ 4071 ||     |                     _________________|            |    |\/ 4071 |||            |    |\/ 4071 ||
        |atan|--------||     |/          ___\     /          ______ |     |     |atan|--------||     |/          ___\     /          ______ |            |atan|--------|||            |atan|--------||
        |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     |     |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     ___    |    \   27   /||     ___    |    \   27   /|
     sin|--------------|     ||- - - -------|*3 /   -- + ---------- |     |  cos|--------------|     ||- - - -------|*3 /   -- + ---------- |   \/ 3 *sin|--------------||   \/ 3 *cos|--------------|
        \      3       /     \\  2      2   / \/    40      360     /     |     \      3       /     \\  2      2   / \/    40      360     /            \      3       /|            \      3       /
x1 = ------------------- + ------------------------------------------ + I*|- ------------------- + ------------------------------------------ - -------------------------| - -------------------------
              2                                3                          \           2                                3                                    6            /               6            
x1=3cos(atan(407127)3)6+re(1(123i2)340+4071i3603)3+sin(atan(407127)3)2+i(cos(atan(407127)3)23sin(atan(407127)3)6+im(1(123i2)340+4071i3603)3)x_{1} = - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(- \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3}\right)
                               /                  1                   \     /                        /                  1                   \                            \                            
          /    /  ______\\   re|--------------------------------------|     |   /    /  ______\\   im|--------------------------------------|            /    /  ______\\|            /    /  ______\\
          |    |\/ 4071 ||     |                     _________________|     |   |    |\/ 4071 ||     |                     _________________|            |    |\/ 4071 |||            |    |\/ 4071 ||
          |atan|--------||     |/          ___\     /          ______ |     |   |atan|--------||     |/          ___\     /          ______ |            |atan|--------|||            |atan|--------||
          |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     |   |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     ___    |    \   27   /||     ___    |    \   27   /|
       sin|--------------|     ||- - + -------|*3 /   -- + ---------- |     |cos|--------------|     ||- - + -------|*3 /   -- + ---------- |   \/ 3 *sin|--------------||   \/ 3 *cos|--------------|
          \      3       /     \\  2      2   / \/    40      360     /     |   \      3       /     \\  2      2   / \/    40      360     /            \      3       /|            \      3       /
x2 = - ------------------- + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| - -------------------------
                2                                3                          \         2                                3                                    6            /               6            
x2=re(1(12+3i2)340+4071i3603)33cos(atan(407127)3)6sin(atan(407127)3)2+i(im(1(12+3i2)340+4071i3603)33sin(atan(407127)3)6+cos(atan(407127)3)2)x_{2} = \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} - \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2}\right)
          _________________                           
         /          ______                            
        /  3    I*\/ 4071                1            
x3 = 3 /   -- + ----------  + ------------------------
     \/    40      360               _________________
                                    /          ______ 
                                   /  3    I*\/ 4071  
                              3*3 /   -- + ---------- 
                                \/    40      360     
x3=13340+4071i3603+340+4071i3603x_{3} = \frac{1}{3 \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}} + \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}
x3 = 1/(3*(3/40 + sqrt(4071)*i/360)^(1/3)) + (3/40 + sqrt(4071)*i/360)^(1/3)
Suma y producto de raíces [src]
suma
                        /                  1                   \     /                          /                  1                   \                            \                                                         /                  1                   \     /                        /                  1                   \                            \                                                                                
   /    /  ______\\   re|--------------------------------------|     |     /    /  ______\\   im|--------------------------------------|            /    /  ______\\|            /    /  ______\\        /    /  ______\\   re|--------------------------------------|     |   /    /  ______\\   im|--------------------------------------|            /    /  ______\\|            /    /  ______\\                                                    
   |    |\/ 4071 ||     |                     _________________|     |     |    |\/ 4071 ||     |                     _________________|            |    |\/ 4071 |||            |    |\/ 4071 ||        |    |\/ 4071 ||     |                     _________________|     |   |    |\/ 4071 ||     |                     _________________|            |    |\/ 4071 |||            |    |\/ 4071 ||                                                    
   |atan|--------||     |/          ___\     /          ______ |     |     |atan|--------||     |/          ___\     /          ______ |            |atan|--------|||            |atan|--------||        |atan|--------||     |/          ___\     /          ______ |     |   |atan|--------||     |/          ___\     /          ______ |            |atan|--------|||            |atan|--------||                                                    
   |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     |     |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     ___    |    \   27   /||     ___    |    \   27   /|        |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     |   |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     ___    |    \   27   /||     ___    |    \   27   /|        _________________                           
sin|--------------|     ||- - - -------|*3 /   -- + ---------- |     |  cos|--------------|     ||- - - -------|*3 /   -- + ---------- |   \/ 3 *sin|--------------||   \/ 3 *cos|--------------|     sin|--------------|     ||- - + -------|*3 /   -- + ---------- |     |cos|--------------|     ||- - + -------|*3 /   -- + ---------- |   \/ 3 *sin|--------------||   \/ 3 *cos|--------------|       /          ______                            
   \      3       /     \\  2      2   / \/    40      360     /     |     \      3       /     \\  2      2   / \/    40      360     /            \      3       /|            \      3       /        \      3       /     \\  2      2   / \/    40      360     /     |   \      3       /     \\  2      2   / \/    40      360     /            \      3       /|            \      3       /      /  3    I*\/ 4071                1            
------------------- + ------------------------------------------ + I*|- ------------------- + ------------------------------------------ - -------------------------| - ------------------------- + - ------------------- + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| - ------------------------- + 3 /   -- + ----------  + ------------------------
         2                                3                          \           2                                3                                    6            /               6                          2                                3                          \         2                                3                                    6            /               6               \/    40      360               _________________
                                                                                                                                                                                                                                                                                                                                                                                                                                       /          ______ 
                                                                                                                                                                                                                                                                                                                                                                                                                                      /  3    I*\/ 4071  
                                                                                                                                                                                                                                                                                                                                                                                                                                 3*3 /   -- + ---------- 
                                                                                                                                                                                                                                                                                                                                                                                                                                   \/    40      360     
(13340+4071i3603+340+4071i3603)+((re(1(12+3i2)340+4071i3603)33cos(atan(407127)3)6sin(atan(407127)3)2+i(im(1(12+3i2)340+4071i3603)33sin(atan(407127)3)6+cos(atan(407127)3)2))+(3cos(atan(407127)3)6+re(1(123i2)340+4071i3603)3+sin(atan(407127)3)2+i(cos(atan(407127)3)23sin(atan(407127)3)6+im(1(123i2)340+4071i3603)3)))\left(\frac{1}{3 \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}} + \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}\right) + \left(\left(\frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} - \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2}\right)\right) + \left(- \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(- \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3}\right)\right)\right)
=
                                                      /                  1                   \     /                  1                   \     /                        /                  1                   \                            \     /                          /                  1                   \                            \                            
                                                    re|--------------------------------------|   re|--------------------------------------|     |   /    /  ______\\   im|--------------------------------------|            /    /  ______\\|     |     /    /  ______\\   im|--------------------------------------|            /    /  ______\\|            /    /  ______\\
                                                      |                     _________________|     |                     _________________|     |   |    |\/ 4071 ||     |                     _________________|            |    |\/ 4071 |||     |     |    |\/ 4071 ||     |                     _________________|            |    |\/ 4071 |||            |    |\/ 4071 ||
                                                      |/          ___\     /          ______ |     |/          ___\     /          ______ |     |   |atan|--------||     |/          ___\     /          ______ |            |atan|--------|||     |     |atan|--------||     |/          ___\     /          ______ |            |atan|--------|||            |atan|--------||
     _________________                                ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     |   |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     ___    |    \   27   /||     |     |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     ___    |    \   27   /||     ___    |    \   27   /|
    /          ______                                 ||- - + -------|*3 /   -- + ---------- |     ||- - - -------|*3 /   -- + ---------- |     |cos|--------------|     ||- - + -------|*3 /   -- + ---------- |   \/ 3 *sin|--------------||     |  cos|--------------|     ||- - - -------|*3 /   -- + ---------- |   \/ 3 *sin|--------------||   \/ 3 *cos|--------------|
   /  3    I*\/ 4071                1                 \\  2      2   / \/    40      360     /     \\  2      2   / \/    40      360     /     |   \      3       /     \\  2      2   / \/    40      360     /            \      3       /|     |     \      3       /     \\  2      2   / \/    40      360     /            \      3       /|            \      3       /
3 /   -- + ----------  + ------------------------ + ------------------------------------------ + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| + I*|- ------------------- + ------------------------------------------ - -------------------------| - -------------------------
\/    40      360               _________________                       3                                            3                          \         2                                3                                    6            /     \           2                                3                                    6            /               3            
                               /          ______                                                                                                                                                                                                                                                                                                                               
                              /  3    I*\/ 4071                                                                                                                                                                                                                                                                                                                                
                         3*3 /   -- + ----------                                                                                                                                                                                                                                                                                                                               
                           \/    40      360                                                                                                                                                                                                                                                                                                                                   
3cos(atan(407127)3)3+re(1(12+3i2)340+4071i3603)3+re(1(123i2)340+4071i3603)3+13340+4071i3603+i(cos(atan(407127)3)23sin(atan(407127)3)6+im(1(123i2)340+4071i3603)3)+i(im(1(12+3i2)340+4071i3603)33sin(atan(407127)3)6+cos(atan(407127)3)2)+340+4071i3603- \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{3} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{1}{3 \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}} + i \left(- \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3}\right) + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2}\right) + \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}
producto
/                        /                  1                   \     /                          /                  1                   \                            \                            \ /                          /                  1                   \     /                        /                  1                   \                            \                            \                                                    
|   /    /  ______\\   re|--------------------------------------|     |     /    /  ______\\   im|--------------------------------------|            /    /  ______\\|            /    /  ______\\| |     /    /  ______\\   re|--------------------------------------|     |   /    /  ______\\   im|--------------------------------------|            /    /  ______\\|            /    /  ______\\|                                                    
|   |    |\/ 4071 ||     |                     _________________|     |     |    |\/ 4071 ||     |                     _________________|            |    |\/ 4071 |||            |    |\/ 4071 ||| |     |    |\/ 4071 ||     |                     _________________|     |   |    |\/ 4071 ||     |                     _________________|            |    |\/ 4071 |||            |    |\/ 4071 |||                                                    
|   |atan|--------||     |/          ___\     /          ______ |     |     |atan|--------||     |/          ___\     /          ______ |            |atan|--------|||            |atan|--------||| |     |atan|--------||     |/          ___\     /          ______ |     |   |atan|--------||     |/          ___\     /          ______ |            |atan|--------|||            |atan|--------|||                                                    
|   |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     |     |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     ___    |    \   27   /||     ___    |    \   27   /|| |     |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     |   |    \   27   /|     ||  1   I*\/ 3 |    /  3    I*\/ 4071  |     ___    |    \   27   /||     ___    |    \   27   /|| /     _________________                           \
|sin|--------------|     ||- - - -------|*3 /   -- + ---------- |     |  cos|--------------|     ||- - - -------|*3 /   -- + ---------- |   \/ 3 *sin|--------------||   \/ 3 *cos|--------------|| |  sin|--------------|     ||- - + -------|*3 /   -- + ---------- |     |cos|--------------|     ||- - + -------|*3 /   -- + ---------- |   \/ 3 *sin|--------------||   \/ 3 *cos|--------------|| |    /          ______                            |
|   \      3       /     \\  2      2   / \/    40      360     /     |     \      3       /     \\  2      2   / \/    40      360     /            \      3       /|            \      3       /| |     \      3       /     \\  2      2   / \/    40      360     /     |   \      3       /     \\  2      2   / \/    40      360     /            \      3       /|            \      3       /| |   /  3    I*\/ 4071                1            |
|------------------- + ------------------------------------------ + I*|- ------------------- + ------------------------------------------ - -------------------------| - -------------------------|*|- ------------------- + ------------------------------------------ + I*|------------------- + ------------------------------------------ - -------------------------| - -------------------------|*|3 /   -- + ----------  + ------------------------|
\         2                                3                          \           2                                3                                    6            /               6            / \           2                                3                          \         2                                3                                    6            /               6            / |\/    40      360               _________________|
                                                                                                                                                                                                                                                                                                                                                                                                        |                               /          ______ |
                                                                                                                                                                                                                                                                                                                                                                                                        |                              /  3    I*\/ 4071  |
                                                                                                                                                                                                                                                                                                                                                                                                        |                         3*3 /   -- + ---------- |
                                                                                                                                                                                                                                                                                                                                                                                                        \                           \/    40      360     /
(3cos(atan(407127)3)6+re(1(123i2)340+4071i3603)3+sin(atan(407127)3)2+i(cos(atan(407127)3)23sin(atan(407127)3)6+im(1(123i2)340+4071i3603)3))(re(1(12+3i2)340+4071i3603)33cos(atan(407127)3)6sin(atan(407127)3)2+i(im(1(12+3i2)340+4071i3603)33sin(atan(407127)3)6+cos(atan(407127)3)2))(13340+4071i3603+340+4071i3603)\left(- \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} + \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(- \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3}\right)\right) \left(\frac{\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} - \frac{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2} + i \left(\frac{\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}}\right)}}{3} - \frac{\sqrt{3} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{6} + \frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}}{2}\right)\right) \left(\frac{1}{3 \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}} + \sqrt[3]{\frac{3}{40} + \frac{\sqrt{4071} i}{360}}\right)
=
/            /      /  ______\\\                                          
|            |      |\/ 4071 |||                                          
|            |2*atan|--------||| /                                    2/3\
|            |      \   27   /|| |   3 ____   3 ____ /         ______\   |
|-12 + 24*cos|----------------||*\20*\/ 45  + \/ 75 *\27 + I*\/ 4071 /   /
\            \       3        //                                          
--------------------------------------------------------------------------
                                _________________                         
                             3 /          ______                          
                        1080*\/  27 + I*\/ 4071                           
(12+24cos(2atan(407127)3))(20453+753(27+4071i)23)108027+4071i3\frac{\left(-12 + 24 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{\sqrt{4071}}{27} \right)}}{3} \right)}\right) \left(20 \sqrt[3]{45} + \sqrt[3]{75} \left(27 + \sqrt{4071} i\right)^{\frac{2}{3}}\right)}{1080 \sqrt[3]{27 + \sqrt{4071} i}}
(-12 + 24*cos(2*atan(sqrt(4071)/27)/3))*(20*45^(1/3) + 75^(1/3)*(27 + i*sqrt(4071))^(2/3))/(1080*(27 + i*sqrt(4071))^(1/3))
Respuesta numérica [src]
x1 = -0.153625697823484
x2 = 1.0679230136897
x3 = -0.914297315866213
x3 = -0.914297315866213