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La ecuación:
Ecuación 3^x=27
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
Ecuación x(x^2+2x+1)=6(x+1)
Ecuación 4x+1=-3x+15
Expresar {x} en función de y en la ecuación:
-6*x-20*y=8
7*x-1*y=0
2*x-8*y=4
2*x-15*y=-1
Expresiones idénticas
uno . trescientos setenta y siete *x^ tres + trece . doscientos noventa y nueve *x^ dos - treinta y tres . trescientos ochenta y cinco *x- ciento noventa y tres . sesenta y nueve = cero
1.377 multiplicar por x al cubo más 13.299 multiplicar por x al cuadrado menos 33.385 multiplicar por x menos 193.69 es igual a 0
uno . trescientos setenta y siete multiplicar por x en el grado tres más trece . doscientos noventa y nueve multiplicar por x en el grado dos menos treinta y tres . trescientos ochenta y cinco multiplicar por x menos ciento noventa y tres . sesenta y nueve es igual a cero
1.377*x3+13.299*x2-33.385*x-193.69=0
1.377*x³+13.299*x²-33.385*x-193.69=0
1.377*x en el grado 3+13.299*x en el grado 2-33.385*x-193.69=0
1.377x^3+13.299x^2-33.385x-193.69=0
1.377x3+13.299x2-33.385x-193.69=0
1.377*x^3+13.299*x^2-33.385*x-193.69=O
Expresiones semejantes
1.377*x^3+13.299*x^2-33.385*x+193.69=0
1.377*x^3-13.299*x^2-33.385*x-193.69=0
1.377*x^3+13.299*x^2+33.385*x-193.69=0

1.377x^3+13.299x^2-33.385*x-193.69=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

      3          2                     
1377*x    13299*x    6677*x   19369    
------- + -------- - ------ - ----- = 0
  1000      1000      200      100

\left(- \frac{6677 x}{200} + \left(\frac{1377 x^{3}}{1000} + \frac{13299 x^{2}}{1000}\right)\right) - \frac{19369}{100} = 0

Simplificar

Teorema de Cardano-Vieta

reescribamos la ecuación

\left(- \frac{6677 x}{200} + \left(\frac{1377 x^{3}}{1000} + \frac{13299 x^{2}}{1000}\right)\right) - \frac{19369}{100} = 0

a x^{3} + b x^{2} + c x + d = 0

como ecuación cúbica reducida

x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0

x^{3} + \frac{4433 x^{2}}{459} - \frac{33385 x}{1377} - \frac{193690}{1377} = 0

p x^{2} + q x + v + x^{3} = 0

donde

p = \frac{b}{a}

p = \frac{4433}{459}

q = \frac{c}{a}

q = - \frac{33385}{1377}

v = \frac{d}{a}

v = - \frac{193690}{1377}

Fórmulas de Cardano-Vieta

x_{1} + x_{2} + x_{3} = - p

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q

x_{1} x_{2} x_{3} = v

x_{1} + x_{2} + x_{3} = - \frac{4433}{459}

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{33385}{1377}

x_{1} x_{2} x_{3} = - \frac{193690}{1377}

Respuesta rápida [src]

                         /                              1                              \     /             /                              1                              \                                                                                                         \                                                                                                         
              34975204*re|-------------------------------------------------------------|     |  34975204*im|-------------------------------------------------------------|                  /    /      ____________________\\                   /    /      ____________________\\|                   /    /      ____________________\\                  /    /      ____________________\\
                         |                     ________________________________________|     |             |                     ________________________________________|                  |    |459*\/ 811748575929195255 ||                   |    |459*\/ 811748575929195255 |||                   |    |459*\/ 811748575929195255 ||                  |    |459*\/ 811748575929195255 ||
                         |/          ___\     /                   ____________________ |     |             |/          ___\     /                   ____________________ |                  |atan|--------------------------||                   |atan|--------------------------|||                   |atan|--------------------------||                  |atan|--------------------------||
                         ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     |             ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     _________    |    \       10758961249        /|     __________    |    \       10758961249        /||     __________    |    \       10758961249        /|     _________    |    \       10758961249        /|
                         ||- - - -------|*3 /   ----------- + ------------------------ |     |             ||- - - -------|*3 /   ----------- + ------------------------ |   \/ 8743801 *sin|--------------------------------|   \/ 26231403 *cos|--------------------------------||   \/ 26231403 *sin|--------------------------------|   \/ 8743801 *cos|--------------------------------|
       4433              \\  2      2   / \/     193405158             421362          /     |             \\  2      2   / \/     193405158             421362          /                  \               3                /                   \               3                /|                   \               3                /                  \               3                /
x1 = - ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- + ------------------------------------------------- + --------------------------------------------------| - -------------------------------------------------- + -------------------------------------------------
       1377                                     632043                                       \                                    632043                                                            1377                                                1377                       /                          1377                                                 1377

x_{1} = - \frac{4433}{1377} - \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + i \left(- \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377}\right)

                         /                              1                              \     /             /                              1                              \                                                                                                         \                                                                                                         
              34975204*re|-------------------------------------------------------------|     |  34975204*im|-------------------------------------------------------------|                   /    /      ____________________\\                  /    /      ____________________\\|                  /    /      ____________________\\                   /    /      ____________________\\
                         |                     ________________________________________|     |             |                     ________________________________________|                   |    |459*\/ 811748575929195255 ||                  |    |459*\/ 811748575929195255 |||                  |    |459*\/ 811748575929195255 ||                   |    |459*\/ 811748575929195255 ||
                         |/          ___\     /                   ____________________ |     |             |/          ___\     /                   ____________________ |                   |atan|--------------------------||                  |atan|--------------------------|||                  |atan|--------------------------||                   |atan|--------------------------||
                         ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     |             ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     __________    |    \       10758961249        /|     _________    |    \       10758961249        /||     _________    |    \       10758961249        /|     __________    |    \       10758961249        /|
                         ||- - + -------|*3 /   ----------- + ------------------------ |     |             ||- - + -------|*3 /   ----------- + ------------------------ |   \/ 26231403 *cos|--------------------------------|   \/ 8743801 *sin|--------------------------------||   \/ 8743801 *cos|--------------------------------|   \/ 26231403 *sin|--------------------------------|
       4433              \\  2      2   / \/     193405158             421362          /     |             \\  2      2   / \/     193405158             421362          /                   \               3                /                  \               3                /|                  \               3                /                   \               3                /
x2 = - ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------| + ------------------------------------------------- + --------------------------------------------------
       1377                                     632043                                       \                                    632043                                                            1377                                                 1377                      /                          1377                                                1377

x_{2} = - \frac{4433}{1377} + \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + i \left(- \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043}\right)

                                                                          ________________________________________
                                                                         /                   ____________________ 
                                                                        /  10758961249   I*\/ 811748575929195255  
                                                                     3 /   ----------- + ------------------------ 
       4433                         34975204                         \/     193405158             421362          
x3 = - ---- - ---------------------------------------------------- - ---------------------------------------------
       1377               ________________________________________                         3                      
                         /                   ____________________                                                 
                        /  10758961249   I*\/ 811748575929195255                                                  
              632043*3 /   ----------- + ------------------------                                                 
                     \/     193405158             421362

x_{3} = - \frac{4433}{1377} - \frac{\sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}{3} - \frac{34975204}{632043 \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}

x3 = -4433/1377 - (10758961249/193405158 + sqrt(811748575929195255)*i/421362)^(1/3)/3 - 34975204/(632043*(10758961249/193405158 + sqrt(811748575929195255)*i/421362)^(1/3))

Suma y producto de raíces [src]

suma

                    /                              1                              \     /             /                              1                              \                                                                                                         \                                                                                                                                /                              1                              \     /             /                              1                              \                                                                                                         \                                                                                                                                                                                                                         
         34975204*re|-------------------------------------------------------------|     |  34975204*im|-------------------------------------------------------------|                  /    /      ____________________\\                   /    /      ____________________\\|                   /    /      ____________________\\                  /    /      ____________________\\            34975204*re|-------------------------------------------------------------|     |  34975204*im|-------------------------------------------------------------|                   /    /      ____________________\\                  /    /      ____________________\\|                  /    /      ____________________\\                   /    /      ____________________\\                                                                                                                
                    |                     ________________________________________|     |             |                     ________________________________________|                  |    |459*\/ 811748575929195255 ||                   |    |459*\/ 811748575929195255 |||                   |    |459*\/ 811748575929195255 ||                  |    |459*\/ 811748575929195255 ||                       |                     ________________________________________|     |             |                     ________________________________________|                   |    |459*\/ 811748575929195255 ||                  |    |459*\/ 811748575929195255 |||                  |    |459*\/ 811748575929195255 ||                   |    |459*\/ 811748575929195255 ||                                                                        ________________________________________
                    |/          ___\     /                   ____________________ |     |             |/          ___\     /                   ____________________ |                  |atan|--------------------------||                   |atan|--------------------------|||                   |atan|--------------------------||                  |atan|--------------------------||                       |/          ___\     /                   ____________________ |     |             |/          ___\     /                   ____________________ |                   |atan|--------------------------||                  |atan|--------------------------|||                  |atan|--------------------------||                   |atan|--------------------------||                                                                       /                   ____________________ 
                    ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     |             ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     _________    |    \       10758961249        /|     __________    |    \       10758961249        /||     __________    |    \       10758961249        /|     _________    |    \       10758961249        /|                       ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     |             ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     __________    |    \       10758961249        /|     _________    |    \       10758961249        /||     _________    |    \       10758961249        /|     __________    |    \       10758961249        /|                                                                      /  10758961249   I*\/ 811748575929195255  
                    ||- - - -------|*3 /   ----------- + ------------------------ |     |             ||- - - -------|*3 /   ----------- + ------------------------ |   \/ 8743801 *sin|--------------------------------|   \/ 26231403 *cos|--------------------------------||   \/ 26231403 *sin|--------------------------------|   \/ 8743801 *cos|--------------------------------|                       ||- - + -------|*3 /   ----------- + ------------------------ |     |             ||- - + -------|*3 /   ----------- + ------------------------ |   \/ 26231403 *cos|--------------------------------|   \/ 8743801 *sin|--------------------------------||   \/ 8743801 *cos|--------------------------------|   \/ 26231403 *sin|--------------------------------|                                                                   3 /   ----------- + ------------------------ 
  4433              \\  2      2   / \/     193405158             421362          /     |             \\  2      2   / \/     193405158             421362          /                  \               3                /                   \               3                /|                   \               3                /                  \               3                /     4433              \\  2      2   / \/     193405158             421362          /     |             \\  2      2   / \/     193405158             421362          /                   \               3                /                  \               3                /|                  \               3                /                   \               3                /     4433                         34975204                         \/     193405158             421362          
- ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- + ------------------------------------------------- + --------------------------------------------------| - -------------------------------------------------- + ------------------------------------------------- + - ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------| + ------------------------------------------------- + -------------------------------------------------- + - ---- - ---------------------------------------------------- - ---------------------------------------------
  1377                                     632043                                       \                                    632043                                                            1377                                                1377                       /                          1377                                                 1377                           1377                                     632043                                       \                                    632043                                                            1377                                                 1377                      /                          1377                                                1377                            1377               ________________________________________                         3                      
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          /                   ____________________                                                 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         /  10758961249   I*\/ 811748575929195255                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               632043*3 /   ----------- + ------------------------                                                 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \/     193405158             421362

\left(\left(- \frac{4433}{1377} - \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + i \left(- \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377}\right)\right) + \left(- \frac{4433}{1377} + \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + i \left(- \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043}\right)\right)\right) + \left(- \frac{4433}{1377} - \frac{\sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}{3} - \frac{34975204}{632043 \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)

                                                                           /                              1                              \              /                              1                              \                                                     /             /                              1                              \                                                                                                         \     /             /                              1                              \                                                                                                         \                                                      
                                                                34975204*re|-------------------------------------------------------------|   34975204*re|-------------------------------------------------------------|                                                     |  34975204*im|-------------------------------------------------------------|                   /    /      ____________________\\                  /    /      ____________________\\|     |  34975204*im|-------------------------------------------------------------|                  /    /      ____________________\\                   /    /      ____________________\\|                    /    /      ____________________\\
                                                                           |                     ________________________________________|              |                     ________________________________________|        ________________________________________     |             |                     ________________________________________|                   |    |459*\/ 811748575929195255 ||                  |    |459*\/ 811748575929195255 |||     |             |                     ________________________________________|                  |    |459*\/ 811748575929195255 ||                   |    |459*\/ 811748575929195255 |||                    |    |459*\/ 811748575929195255 ||
                                                                           |/          ___\     /                   ____________________ |              |/          ___\     /                   ____________________ |       /                   ____________________      |             |/          ___\     /                   ____________________ |                   |atan|--------------------------||                  |atan|--------------------------|||     |             |/          ___\     /                   ____________________ |                  |atan|--------------------------||                   |atan|--------------------------|||                    |atan|--------------------------||
                                                                           ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |              ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |      /  10758961249   I*\/ 811748575929195255       |             ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     __________    |    \       10758961249        /|     _________    |    \       10758961249        /||     |             ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     _________    |    \       10758961249        /|     __________    |    \       10758961249        /||       _________    |    \       10758961249        /|
                                                                           ||- - + -------|*3 /   ----------- + ------------------------ |              ||- - - -------|*3 /   ----------- + ------------------------ |   3 /   ----------- + ------------------------      |             ||- - + -------|*3 /   ----------- + ------------------------ |   \/ 26231403 *cos|--------------------------------|   \/ 8743801 *sin|--------------------------------||     |             ||- - - -------|*3 /   ----------- + ------------------------ |   \/ 8743801 *sin|--------------------------------|   \/ 26231403 *cos|--------------------------------||   2*\/ 8743801 *cos|--------------------------------|
  4433                         34975204                                    \\  2      2   / \/     193405158             421362          /              \\  2      2   / \/     193405158             421362          /   \/     193405158             421362               |             \\  2      2   / \/     193405158             421362          /                   \               3                /                  \               3                /|     |             \\  2      2   / \/     193405158             421362          /                  \               3                /                   \               3                /|                    \               3                /
- ---- - ---------------------------------------------------- - -------------------------------------------------------------------------- - -------------------------------------------------------------------------- - --------------------------------------------- + I*|- -------------------------------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------| + I*|- -------------------------------------------------------------------------- + ------------------------------------------------- + --------------------------------------------------| + ---------------------------------------------------
  459                ________________________________________                                     632043                                                                       632043                                                           3                           \                                    632043                                                            1377                                                 1377                      /     \                                    632043                                                            1377                                                1377                       /                           1377                       
                    /                   ____________________                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
                   /  10758961249   I*\/ 811748575929195255                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          
         632043*3 /   ----------- + ------------------------                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
                \/     193405158             421362

- \frac{4433}{459} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{2 \sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{\sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}{3} + i \left(- \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043}\right) + i \left(- \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377}\right) - \frac{34975204}{632043 \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}

producto

/                    /                              1                              \     /             /                              1                              \                                                                                                         \                                                                                                         \ /                    /                              1                              \     /             /                              1                              \                                                                                                         \                                                                                                         \                                                                                                                
|         34975204*re|-------------------------------------------------------------|     |  34975204*im|-------------------------------------------------------------|                  /    /      ____________________\\                   /    /      ____________________\\|                   /    /      ____________________\\                  /    /      ____________________\\| |         34975204*re|-------------------------------------------------------------|     |  34975204*im|-------------------------------------------------------------|                   /    /      ____________________\\                  /    /      ____________________\\|                  /    /      ____________________\\                   /    /      ____________________\\|                                                                                                                
|                    |                     ________________________________________|     |             |                     ________________________________________|                  |    |459*\/ 811748575929195255 ||                   |    |459*\/ 811748575929195255 |||                   |    |459*\/ 811748575929195255 ||                  |    |459*\/ 811748575929195255 ||| |                    |                     ________________________________________|     |             |                     ________________________________________|                   |    |459*\/ 811748575929195255 ||                  |    |459*\/ 811748575929195255 |||                  |    |459*\/ 811748575929195255 ||                   |    |459*\/ 811748575929195255 ||| /                                                                     ________________________________________\
|                    |/          ___\     /                   ____________________ |     |             |/          ___\     /                   ____________________ |                  |atan|--------------------------||                   |atan|--------------------------|||                   |atan|--------------------------||                  |atan|--------------------------||| |                    |/          ___\     /                   ____________________ |     |             |/          ___\     /                   ____________________ |                   |atan|--------------------------||                  |atan|--------------------------|||                  |atan|--------------------------||                   |atan|--------------------------||| |                                                                    /                   ____________________ |
|                    ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     |             ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     _________    |    \       10758961249        /|     __________    |    \       10758961249        /||     __________    |    \       10758961249        /|     _________    |    \       10758961249        /|| |                    ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     |             ||  1   I*\/ 3 |    /  10758961249   I*\/ 811748575929195255  |     __________    |    \       10758961249        /|     _________    |    \       10758961249        /||     _________    |    \       10758961249        /|     __________    |    \       10758961249        /|| |                                                                   /  10758961249   I*\/ 811748575929195255  |
|                    ||- - - -------|*3 /   ----------- + ------------------------ |     |             ||- - - -------|*3 /   ----------- + ------------------------ |   \/ 8743801 *sin|--------------------------------|   \/ 26231403 *cos|--------------------------------||   \/ 26231403 *sin|--------------------------------|   \/ 8743801 *cos|--------------------------------|| |                    ||- - + -------|*3 /   ----------- + ------------------------ |     |             ||- - + -------|*3 /   ----------- + ------------------------ |   \/ 26231403 *cos|--------------------------------|   \/ 8743801 *sin|--------------------------------||   \/ 8743801 *cos|--------------------------------|   \/ 26231403 *sin|--------------------------------|| |                                                                3 /   ----------- + ------------------------ |
|  4433              \\  2      2   / \/     193405158             421362          /     |             \\  2      2   / \/     193405158             421362          /                  \               3                /                   \               3                /|                   \               3                /                  \               3                /| |  4433              \\  2      2   / \/     193405158             421362          /     |             \\  2      2   / \/     193405158             421362          /                   \               3                /                  \               3                /|                  \               3                /                   \               3                /| |  4433                         34975204                         \/     193405158             421362          |
|- ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- + ------------------------------------------------- + --------------------------------------------------| - -------------------------------------------------- + -------------------------------------------------|*|- ---- - -------------------------------------------------------------------------- + I*|- -------------------------------------------------------------------------- - -------------------------------------------------- + -------------------------------------------------| + ------------------------------------------------- + --------------------------------------------------|*|- ---- - ---------------------------------------------------- - ---------------------------------------------|
\  1377                                     632043                                       \                                    632043                                                            1377                                                1377                       /                          1377                                                 1377                      / \  1377                                     632043                                       \                                    632043                                                            1377                                                 1377                      /                          1377                                                1377                       / |  1377               ________________________________________                         3                      |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |                    /                   ____________________                                                 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |                   /  10758961249   I*\/ 811748575929195255                                                  |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |         632043*3 /   ----------- + ------------------------                                                 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      \                \/     193405158             421362                                                          /

\left(- \frac{4433}{1377} - \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + i \left(- \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377}\right)\right) \left(- \frac{4433}{1377} + \frac{\sqrt{26231403} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043} + i \left(- \frac{\sqrt{26231403} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} + \frac{\sqrt{8743801} \sin{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}}{1377} - \frac{34975204 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)}}{632043}\right)\right) \left(- \frac{4433}{1377} - \frac{\sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}{3} - \frac{34975204}{632043 \sqrt[3]{\frac{10758961249}{193405158} + \frac{\sqrt{811748575929195255} i}{421362}}}\right)

                                                                                                                                 /                       /      /      ____________________\\                        /    /      ____________________\\\
                                                                                                                                 |                       |      |459*\/ 811748575929195255 ||                        |    |459*\/ 811748575929195255 |||
/                    ____________________________________________ /               ____________________________________________\\ |                       |2*atan|--------------------------||                        |atan|--------------------------|||
|         3 ___   3 /                       ____________________  |        2/3 3 /                       ____________________ || |                       |      \       10758961249        /|           _________    |    \       10758961249        /||
\69950408*\/ 2  + \/  10758961249 + 459*I*\/ 811748575929195255  *\8866 + 2   *\/  10758961249 + 459*I*\/ 811748575929195255  //*|15323715 - 69950408*cos|----------------------------------| + 17732*\/ 8743801 *cos|--------------------------------||
                                                                                                                                 \                       \                3                 /                        \               3                //
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                             ____________________________________________                                                                                               
                                                                                                          3 /                       ____________________                                                                                                
                                                                                               5221939266*\/  10758961249 + 459*I*\/ 811748575929195255

\frac{\left(69950408 \sqrt[3]{2} + \left(8866 + 2^{\frac{2}{3}} \sqrt[3]{10758961249 + 459 \sqrt{811748575929195255} i}\right) \sqrt[3]{10758961249 + 459 \sqrt{811748575929195255} i}\right) \left(- 69950408 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)} + 15323715 + 17732 \sqrt{8743801} \cos{\left(\frac{\operatorname{atan}{\left(\frac{459 \sqrt{811748575929195255}}{10758961249} \right)}}{3} \right)}\right)}{5221939266 \sqrt[3]{10758961249 + 459 \sqrt{811748575929195255} i}}

(69950408*2^(1/3) + (10758961249 + 459*i*sqrt(811748575929195255))^(1/3)*(8866 + 2^(2/3)*(10758961249 + 459*i*sqrt(811748575929195255))^(1/3)))*(15323715 - 69950408*cos(2*atan(459*sqrt(811748575929195255)/10758961249)/3) + 17732*sqrt(8743801)*cos(atan(459*sqrt(811748575929195255)/10758961249)/3))/(5221939266*(10758961249 + 459*i*sqrt(811748575929195255))^(1/3))

Respuesta numérica [src]

x1 = -10.695141588861

x2 = -3.14484442976019

x3 = 4.18203394890436

x3 = 4.18203394890436

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1.377*x^3+13.299*x^2-33.385*x-193.69=0 la ecuación

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1.377x^3+13.299x^2-33.385*x-193.69=0 la ecuación