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La ecuación:
Ecuación 6x+1=-4x
Ecuación x+y-3=0
Ecuación x^2=-3
Ecuación 9-7(x+3)=5-6x
Expresar {x} en función de y en la ecuación:
-11*x+9*y=-20
5*x-14*y=-15
-10*x+15*y=10
-9*x-6*y=12
Factorizar el polinomio:
x^3+2*x-11
Expresiones idénticas
x^ tres + dos *x- once = cero
x al cubo más 2 multiplicar por x menos 11 es igual a 0
x en el grado tres más dos multiplicar por x menos once es igual a cero
x3+2*x-11=0
x³+2*x-11=0
x en el grado 3+2*x-11=0
x^3+2x-11=0
x3+2x-11=0
x^3+2*x-11=O
Expresiones semejantes
x^3-2*x-11=0
x^3+2*x+11=0

x^3+2*x-11=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3               
x  + 2*x - 11 = 0

\left(x^{3} + 2 x\right) - 11 = 0

Simplificar

Teorema de Cardano-Vieta

es ecuación cúbica reducida

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

donde

p = \frac{b}{a}

p = 0

q = \frac{c}{a}

q = 2

v = \frac{d}{a}

v = -11

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} = 0

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

x_{1} x_{2} x_{3} = -11

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

            _______________                              /             _______________                         \
           /        ______                               |            /        ______                          |
          /  11   \/ 9897                                |    ___    /  11   \/ 9897                           |
       3 /   -- + --------                               |  \/ 3 *3 /   -- + --------              ___         |
       \/    2       18                 1                |        \/    2       18               \/ 3          |
x1 = - -------------------- + ---------------------- + I*|- -------------------------- - ----------------------|
                2                    _______________     |              2                       _______________|
                                    /        ______      |                                     /        ______ |
                                   /  11   \/ 9897       |                                    /  11   \/ 9897  |
                              3*3 /   -- + --------      |                               3*3 /   -- + -------- |
                                \/    2       18         \                                 \/    2       18    /

x_{1} = - \frac{\sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}\right)

            _______________                              /           _______________                         \
           /        ______                               |          /        ______                          |
          /  11   \/ 9897                                |  ___    /  11   \/ 9897                           |
       3 /   -- + --------                               |\/ 3 *3 /   -- + --------              ___         |
       \/    2       18                 1                |      \/    2       18               \/ 3          |
x2 = - -------------------- + ---------------------- + I*|-------------------------- + ----------------------|
                2                    _______________     |            2                       _______________|
                                    /        ______      |                                   /        ______ |
                                   /  11   \/ 9897       |                                  /  11   \/ 9897  |
                              3*3 /   -- + --------      |                             3*3 /   -- + -------- |
                                \/    2       18         \                               \/    2       18    /

x_{2} = - \frac{\sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2}\right)

          _______________                         
         /        ______                          
        /  11   \/ 9897               2           
x3 = 3 /   -- + --------  - ----------------------
     \/    2       18              _______________
                                  /        ______ 
                                 /  11   \/ 9897  
                            3*3 /   -- + -------- 
                              \/    2       18

x_{3} = - \frac{2}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}

x3 = -2/(3*(11/2 + sqrt(9897)/18)^(1/3)) + (11/2 + sqrt(9897)/18)^(1/3)

Suma y producto de raíces [src]

suma

       _______________                              /             _______________                         \          _______________                              /           _______________                         \                                                
      /        ______                               |            /        ______                          |         /        ______                               |          /        ______                          |                                                
     /  11   \/ 9897                                |    ___    /  11   \/ 9897                           |        /  11   \/ 9897                                |  ___    /  11   \/ 9897                           |        _______________                         
  3 /   -- + --------                               |  \/ 3 *3 /   -- + --------              ___         |     3 /   -- + --------                               |\/ 3 *3 /   -- + --------              ___         |       /        ______                          
  \/    2       18                 1                |        \/    2       18               \/ 3          |     \/    2       18                 1                |      \/    2       18               \/ 3          |      /  11   \/ 9897               2           
- -------------------- + ---------------------- + I*|- -------------------------- - ----------------------| + - -------------------- + ---------------------- + I*|-------------------------- + ----------------------| + 3 /   -- + --------  - ----------------------
           2                    _______________     |              2                       _______________|              2                    _______________     |            2                       _______________|   \/    2       18              _______________
                               /        ______      |                                     /        ______ |                                  /        ______      |                                   /        ______ |                                /        ______ 
                              /  11   \/ 9897       |                                    /  11   \/ 9897  |                                 /  11   \/ 9897       |                                  /  11   \/ 9897  |                               /  11   \/ 9897  
                         3*3 /   -- + --------      |                               3*3 /   -- + -------- |                            3*3 /   -- + --------      |                             3*3 /   -- + -------- |                          3*3 /   -- + -------- 
                           \/    2       18         \                                 \/    2       18    /                              \/    2       18         \                               \/    2       18    /                            \/    2       18

\left(- \frac{2}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2}\right)\right)\right)

  /           _______________                         \     /             _______________                         \
  |          /        ______                          |     |            /        ______                          |
  |  ___    /  11   \/ 9897                           |     |    ___    /  11   \/ 9897                           |
  |\/ 3 *3 /   -- + --------              ___         |     |  \/ 3 *3 /   -- + --------              ___         |
  |      \/    2       18               \/ 3          |     |        \/    2       18               \/ 3          |
I*|-------------------------- + ----------------------| + I*|- -------------------------- - ----------------------|
  |            2                       _______________|     |              2                       _______________|
  |                                   /        ______ |     |                                     /        ______ |
  |                                  /  11   \/ 9897  |     |                                    /  11   \/ 9897  |
  |                             3*3 /   -- + -------- |     |                               3*3 /   -- + -------- |
  \                               \/    2       18    /     \                                 \/    2       18    /

i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}\right) + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2}\right)

producto

/       _______________                              /             _______________                         \\ /       _______________                              /           _______________                         \\                                                
|      /        ______                               |            /        ______                          || |      /        ______                               |          /        ______                          ||                                                
|     /  11   \/ 9897                                |    ___    /  11   \/ 9897                           || |     /  11   \/ 9897                                |  ___    /  11   \/ 9897                           || /     _______________                         \
|  3 /   -- + --------                               |  \/ 3 *3 /   -- + --------              ___         || |  3 /   -- + --------                               |\/ 3 *3 /   -- + --------              ___         || |    /        ______                          |
|  \/    2       18                 1                |        \/    2       18               \/ 3          || |  \/    2       18                 1                |      \/    2       18               \/ 3          || |   /  11   \/ 9897               2           |
|- -------------------- + ---------------------- + I*|- -------------------------- - ----------------------||*|- -------------------- + ---------------------- + I*|-------------------------- + ----------------------||*|3 /   -- + --------  - ----------------------|
|           2                    _______________     |              2                       _______________|| |           2                    _______________     |            2                       _______________|| |\/    2       18              _______________|
|                               /        ______      |                                     /        ______ || |                               /        ______      |                                   /        ______ || |                             /        ______ |
|                              /  11   \/ 9897       |                                    /  11   \/ 9897  || |                              /  11   \/ 9897       |                                  /  11   \/ 9897  || |                            /  11   \/ 9897  |
|                         3*3 /   -- + --------      |                               3*3 /   -- + -------- || |                         3*3 /   -- + --------      |                             3*3 /   -- + -------- || |                       3*3 /   -- + -------- |
\                           \/    2       18         \                                 \/    2       18    // \                           \/    2       18         \                               \/    2       18    // \                         \/    2       18    /

\left(- \frac{\sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + i \left(\frac{\sqrt{3}}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} + \frac{1}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}{2} - \frac{\sqrt{3}}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}}\right)\right) \left(- \frac{2}{3 \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}} + \sqrt[3]{\frac{11}{2} + \frac{\sqrt{9897}}{18}}\right)

11

Respuesta numérica [src]

x1 = -0.963135157148397 + 2.1869814797583*i

x2 = -0.963135157148397 - 2.1869814797583*i

x3 = 1.92627031429679

x3 = 1.92627031429679

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Expresiones idénticas

Expresiones semejantes

x^3+2*x-11=0 la ecuación

Solución numérica:

Solución