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La ecuación:
Ecuación 56/x=(10+6)/2
Ecuación 15-4(7-x)=11
Ecuación 3^8-x=27
Ecuación 6,4(y-12,8)=3,2
Expresar {x} en función de y en la ecuación:
20*x+7*y=-9
-13*x-10*y=5
15*x+7*y=2
20*x+9*y=17
Integral de d{x}:
x^3+x+3
Expresiones idénticas
x^ tres +x+ tres = cero
x al cubo más x más 3 es igual a 0
x en el grado tres más x más tres es igual a cero
x3+x+3=0
x³+x+3=0
x en el grado 3+x+3=0
x^3+x+3=O
Expresiones semejantes
x^3-x+3=0
x^3+x-3=0

x^3+x+3=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3            
x  + x + 3 = 0

\left(x^{3} + x\right) + 3 = 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 = 1

v = \frac{d}{a}

v = 3

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} = 1

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

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

                                 ________________     /                                     ________________\                                    ________________     /                                       ________________\                                ________________
                                /          _____      |                                    /          _____ |                                   /          _____      |                                      /          _____ |                               /          _____ 
                               /  81   3*\/ 741       |                            ___    /  81   3*\/ 741  |                                  /  81   3*\/ 741       |                              ___    /  81   3*\/ 741  |                              /  81   3*\/ 741  
                            3 /   -- + ---------      |           ___            \/ 3 *3 /   -- + --------- |                               3 /   -- + ---------      |             ___            \/ 3 *3 /   -- + --------- |                           3 /   -- + --------- 
             1              \/    2        2          |         \/ 3                   \/    2        2     |                1              \/    2        2          |           \/ 3                   \/    2        2     |             1             \/    2        2     
- ----------------------- + --------------------- + I*|----------------------- + ---------------------------| + - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------| + --------------------- - ---------------------
         ________________             6               |       ________________                6             |            ________________             6               |         ________________                6             |        ________________             3          
        /          _____                              |      /          _____                               |           /          _____                              |        /          _____                               |       /          _____                         
       /  81   3*\/ 741                               |     /  81   3*\/ 741                                |          /  81   3*\/ 741                               |       /  81   3*\/ 741                                |      /  81   3*\/ 741                          
  2*3 /   -- + ---------                              |2*3 /   -- + ---------                               |     2*3 /   -- + ---------                              |  2*3 /   -- + ---------                               |   3 /   -- + ---------                         
    \/    2        2                                  \  \/    2        2                                   /       \/    2        2                                  \    \/    2        2                                   /   \/    2        2

\left(- \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{3} + \frac{1}{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right) + \left(\left(- \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right)\right) + \left(- \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6}\right)\right)\right)

  /                                     ________________\     /                                       ________________\
  |                                    /          _____ |     |                                      /          _____ |
  |                            ___    /  81   3*\/ 741  |     |                              ___    /  81   3*\/ 741  |
  |           ___            \/ 3 *3 /   -- + --------- |     |             ___            \/ 3 *3 /   -- + --------- |
  |         \/ 3                   \/    2        2     |     |           \/ 3                   \/    2        2     |
I*|----------------------- + ---------------------------| + I*|- ----------------------- - ---------------------------|
  |       ________________                6             |     |         ________________                6             |
  |      /          _____                               |     |        /          _____                               |
  |     /  81   3*\/ 741                                |     |       /  81   3*\/ 741                                |
  |2*3 /   -- + ---------                               |     |  2*3 /   -- + ---------                               |
  \  \/    2        2                                   /     \    \/    2        2                                   /

i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right) + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6}\right)

producto

/                                 ________________     /                                     ________________\\ /                                 ________________     /                                       ________________\\ /                             ________________\
|                                /          _____      |                                    /          _____ || |                                /          _____      |                                      /          _____ || |                            /          _____ |
|                               /  81   3*\/ 741       |                            ___    /  81   3*\/ 741  || |                               /  81   3*\/ 741       |                              ___    /  81   3*\/ 741  || |                           /  81   3*\/ 741  |
|                            3 /   -- + ---------      |           ___            \/ 3 *3 /   -- + --------- || |                            3 /   -- + ---------      |             ___            \/ 3 *3 /   -- + --------- || |                        3 /   -- + --------- |
|             1              \/    2        2          |         \/ 3                   \/    2        2     || |             1              \/    2        2          |           \/ 3                   \/    2        2     || |          1             \/    2        2     |
|- ----------------------- + --------------------- + I*|----------------------- + ---------------------------||*|- ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------||*|--------------------- - ---------------------|
|         ________________             6               |       ________________                6             || |         ________________             6               |         ________________                6             || |     ________________             3          |
|        /          _____                              |      /          _____                               || |        /          _____                              |        /          _____                               || |    /          _____                         |
|       /  81   3*\/ 741                               |     /  81   3*\/ 741                                || |       /  81   3*\/ 741                               |       /  81   3*\/ 741                                || |   /  81   3*\/ 741                          |
|  2*3 /   -- + ---------                              |2*3 /   -- + ---------                               || |  2*3 /   -- + ---------                              |  2*3 /   -- + ---------                               || |3 /   -- + ---------                         |
\    \/    2        2                                  \  \/    2        2                                   // \    \/    2        2                                  \    \/    2        2                                   // \\/    2        2                             /

\left(- \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6}\right)\right) \left(- \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{3} + \frac{1}{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right)

           __________________              ________________                           2/3                __________________                          2/3                                 2/3                     ________________                                     2/3
        3 /            _____        2/3 3 /          _____      3 ___ /         _____\          _____ 3 /            _____      3 ____ /       _____\      3 ___   _____ /         _____\         2/3   _____ 3 /          _____    3 ___ 6 ___   _____ /       _____\   
     81*\/  324 + 12*\/ 741     81*2   *\/  81 + 3*\/ 741     3*\/ 2 *\81 + 3*\/ 741 /      3*\/ 741 *\/  324 + 12*\/ 741     3*\/ 18 *\27 + \/ 741 /      \/ 2 *\/ 741 *\81 + 3*\/ 741 /      3*2   *\/ 741 *\/  81 + 3*\/ 741     \/ 2 *\/ 3 *\/ 247 *\27 + \/ 741 /   
-3 + ------------------------ - --------------------------- - --------------------------- - ------------------------------- + -------------------------- + --------------------------------- + ---------------------------------- - -------------------------------------
                32                           32                            8                               32                             8                                72                                  32                                     24

- \frac{3 \sqrt{741} \sqrt[3]{324 + 12 \sqrt{741}}}{32} - \frac{81 \cdot 2^{\frac{2}{3}} \sqrt[3]{81 + 3 \sqrt{741}}}{32} - \frac{\sqrt[3]{2} \sqrt{247} \sqrt[6]{3} \left(27 + \sqrt{741}\right)^{\frac{2}{3}}}{24} - \frac{3 \sqrt[3]{2} \left(81 + 3 \sqrt{741}\right)^{\frac{2}{3}}}{8} - 3 + \frac{3 \sqrt[3]{18} \left(27 + \sqrt{741}\right)^{\frac{2}{3}}}{8} + \frac{\sqrt[3]{2} \sqrt{741} \left(81 + 3 \sqrt{741}\right)^{\frac{2}{3}}}{72} + \frac{81 \sqrt[3]{324 + 12 \sqrt{741}}}{32} + \frac{3 \cdot 2^{\frac{2}{3}} \sqrt{741} \sqrt[3]{81 + 3 \sqrt{741}}}{32}

-3 + 81*(324 + 12*sqrt(741))^(1/3)/32 - 81*2^(2/3)*(81 + 3*sqrt(741))^(1/3)/32 - 3*2^(1/3)*(81 + 3*sqrt(741))^(2/3)/8 - 3*sqrt(741)*(324 + 12*sqrt(741))^(1/3)/32 + 3*18^(1/3)*(27 + sqrt(741))^(2/3)/8 + 2^(1/3)*sqrt(741)*(81 + 3*sqrt(741))^(2/3)/72 + 3*2^(2/3)*sqrt(741)*(81 + 3*sqrt(741))^(1/3)/32 - 2^(1/3)*3^(1/6)*sqrt(247)*(27 + sqrt(741))^(2/3)/24

Respuesta rápida [src]

                                      ________________     /                                     ________________\
                                     /          _____      |                                    /          _____ |
                                    /  81   3*\/ 741       |                            ___    /  81   3*\/ 741  |
                                 3 /   -- + ---------      |           ___            \/ 3 *3 /   -- + --------- |
                  1              \/    2        2          |         \/ 3                   \/    2        2     |
x1 = - ----------------------- + --------------------- + I*|----------------------- + ---------------------------|
              ________________             6               |       ________________                6             |
             /          _____                              |      /          _____                               |
            /  81   3*\/ 741                               |     /  81   3*\/ 741                                |
       2*3 /   -- + ---------                              |2*3 /   -- + ---------                               |
         \/    2        2                                  \  \/    2        2                                   /

x_{1} = - \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + i \left(\frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6}\right)

                                      ________________     /                                       ________________\
                                     /          _____      |                                      /          _____ |
                                    /  81   3*\/ 741       |                              ___    /  81   3*\/ 741  |
                                 3 /   -- + ---------      |             ___            \/ 3 *3 /   -- + --------- |
                  1              \/    2        2          |           \/ 3                   \/    2        2     |
x2 = - ----------------------- + --------------------- + I*|- ----------------------- - ---------------------------|
              ________________             6               |         ________________                6             |
             /          _____                              |        /          _____                               |
            /  81   3*\/ 741                               |       /  81   3*\/ 741                                |
       2*3 /   -- + ---------                              |  2*3 /   -- + ---------                               |
         \/    2        2                                  \    \/    2        2                                   /

x_{2} = - \frac{1}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}} + \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{6} - \frac{\sqrt{3}}{2 \sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}\right)

                                  ________________
                                 /          _____ 
                                /  81   3*\/ 741  
                             3 /   -- + --------- 
               1             \/    2        2     
x3 = --------------------- - ---------------------
          ________________             3          
         /          _____                         
        /  81   3*\/ 741                          
     3 /   -- + ---------                         
     \/    2        2

x_{3} = - \frac{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}{3} + \frac{1}{\sqrt[3]{\frac{81}{2} + \frac{3 \sqrt{741}}{2}}}

x3 = -(81/2 + 3*sqrt(741)/2)^(1/3)/3 + (81/2 + 3*sqrt(741)/2)^(-1/3)

Respuesta numérica [src]

x1 = 0.606705831381115 + 1.45061224918844*i

x2 = 0.606705831381115 - 1.45061224918844*i

x3 = -1.21341166276223

x3 = -1.21341166276223

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Expresiones idénticas

Expresiones semejantes

x^3+x+3=0 la ecuación

Solución numérica:

Solución