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La ecuación:
Ecuación 2*x^2-7*x+12=0
Ecuación 6(x-9)=x+5
Ecuación n^2-3n-108=0
Ecuación x^3+3*x=1
Expresar {x} en función de y en la ecuación:
9*x+7*y=4
-1*x+7*y=-11
8*x+13*y=2
4*x-2*y=-12
Expresiones idénticas
X^ tres +x^ dos + dos *x+ cinco = cero
X al cubo más x al cuadrado más 2 multiplicar por x más 5 es igual a 0
X en el grado tres más x en el grado dos más dos multiplicar por x más cinco es igual a cero
X3+x2+2*x+5=0
X³+x²+2*x+5=0
X en el grado 3+x en el grado 2+2*x+5=0
X^3+x^2+2x+5=0
X3+x2+2x+5=0
X^3+x^2+2*x+5=O
Expresiones semejantes
X^3+x^2-2*x+5=0
X^3-x^2+2*x+5=0
X^3+x^2+2*x-5=0

X^3+x^2+2*x+5=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3    2              
x  + x  + 2*x + 5 = 0

$$\left(2 x + \left(x^{3} + x^{2}\right)\right) + 5 = 0$$

Simplificar

Teorema de Cardano-Vieta

es ecuación cúbica reducida
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = 2$$
$$v = \frac{d}{a}$$
$$v = 5$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = -1$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 2$$
$$x_{1} x_{2} x_{3} = 5$$

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

                                           _________________     /           _________________                           \
                                          /           _____      |          /           _____                            |
                                         /  119   9*\/ 181       |  ___    /  119   9*\/ 181                             |
                                      3 /   --- + ---------      |\/ 3 *3 /   --- + ---------                ___         |
       1              5               \/     2        2          |      \/     2        2                5*\/ 3          |
x1 = - - - ------------------------ + ---------------------- + I*|---------------------------- + ------------------------|
       3          _________________             6                |             6                        _________________|
                 /           _____                               |                                     /           _____ |
                /  119   9*\/ 181                                |                                    /  119   9*\/ 181  |
           6*3 /   --- + ---------                               |                               6*3 /   --- + --------- |
             \/     2        2                                   \                                 \/     2        2     /

$$x_{1} = - \frac{1}{3} - \frac{5}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} + i \left(\frac{5 \sqrt{3}}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6}\right)$$

                                           _________________     /                                        _________________\
                                          /           _____      |                                       /           _____ |
                                         /  119   9*\/ 181       |                               ___    /  119   9*\/ 181  |
                                      3 /   --- + ---------      |              ___            \/ 3 *3 /   --- + --------- |
       1              5               \/     2        2          |          5*\/ 3                   \/     2        2     |
x2 = - - - ------------------------ + ---------------------- + I*|- ------------------------ - ----------------------------|
       3          _________________             6                |         _________________                6              |
                 /           _____                               |        /           _____                                |
                /  119   9*\/ 181                                |       /  119   9*\/ 181                                 |
           6*3 /   --- + ---------                               |  6*3 /   --- + ---------                                |
             \/     2        2                                   \    \/     2        2                                    /

$$x_{2} = - \frac{1}{3} - \frac{5}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} - \frac{5 \sqrt{3}}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}\right)$$

                _________________                           
               /           _____                            
              /  119   9*\/ 181                             
           3 /   --- + ---------                            
       1   \/     2        2                   5            
x3 = - - - ---------------------- + ------------------------
       3             3                     _________________
                                          /           _____ 
                                         /  119   9*\/ 181  
                                    3*3 /   --- + --------- 
                                      \/     2        2

$$x_{3} = - \frac{\sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{3} - \frac{1}{3} + \frac{5}{3 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}$$

x3 = -(119/2 + 9*sqrt(181)/2)^(1/3)/3 - 1/3 + 5/(3*(119/2 + 9*sqrt(181)/2)^(1/3))

Suma y producto de raíces [src]

suma

                                      _________________     /           _________________                           \                                         _________________     /                                        _________________\              _________________                           
                                     /           _____      |          /           _____                            |                                        /           _____      |                                       /           _____ |             /           _____                            
                                    /  119   9*\/ 181       |  ___    /  119   9*\/ 181                             |                                       /  119   9*\/ 181       |                               ___    /  119   9*\/ 181  |            /  119   9*\/ 181                             
                                 3 /   --- + ---------      |\/ 3 *3 /   --- + ---------                ___         |                                    3 /   --- + ---------      |              ___            \/ 3 *3 /   --- + --------- |         3 /   --- + ---------                            
  1              5               \/     2        2          |      \/     2        2                5*\/ 3          |     1              5               \/     2        2          |          5*\/ 3                   \/     2        2     |     1   \/     2        2                   5            
- - - ------------------------ + ---------------------- + I*|---------------------------- + ------------------------| + - - - ------------------------ + ---------------------- + I*|- ------------------------ - ----------------------------| + - - - ---------------------- + ------------------------
  3          _________________             6                |             6                        _________________|     3          _________________             6                |         _________________                6              |     3             3                     _________________
            /           _____                               |                                     /           _____ |               /           _____                               |        /           _____                                |                                        /           _____ 
           /  119   9*\/ 181                                |                                    /  119   9*\/ 181  |              /  119   9*\/ 181                                |       /  119   9*\/ 181                                 |                                       /  119   9*\/ 181  
      6*3 /   --- + ---------                               |                               6*3 /   --- + --------- |         6*3 /   --- + ---------                               |  6*3 /   --- + ---------                                |                                  3*3 /   --- + --------- 
        \/     2        2                                   \                                 \/     2        2     /           \/     2        2                                   \    \/     2        2                                    /                                    \/     2        2

$$\left(- \frac{\sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{3} - \frac{1}{3} + \frac{5}{3 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}\right) + \left(\left(- \frac{1}{3} - \frac{5}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} - \frac{5 \sqrt{3}}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}\right)\right) + \left(- \frac{1}{3} - \frac{5}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} + i \left(\frac{5 \sqrt{3}}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6}\right)\right)\right)$$

       /                                        _________________\     /           _________________                           \
       |                                       /           _____ |     |          /           _____                            |
       |                               ___    /  119   9*\/ 181  |     |  ___    /  119   9*\/ 181                             |
       |              ___            \/ 3 *3 /   --- + --------- |     |\/ 3 *3 /   --- + ---------                ___         |
       |          5*\/ 3                   \/     2        2     |     |      \/     2        2                5*\/ 3          |
-1 + I*|- ------------------------ - ----------------------------| + I*|---------------------------- + ------------------------|
       |         _________________                6              |     |             6                        _________________|
       |        /           _____                                |     |                                     /           _____ |
       |       /  119   9*\/ 181                                 |     |                                    /  119   9*\/ 181  |
       |  6*3 /   --- + ---------                                |     |                               6*3 /   --- + --------- |
       \    \/     2        2                                    /     \                                 \/     2        2     /

$$-1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} - \frac{5 \sqrt{3}}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}\right) + i \left(\frac{5 \sqrt{3}}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6}\right)$$

producto

/                                      _________________     /           _________________                           \\ /                                      _________________     /                                        _________________\\ /           _________________                           \
|                                     /           _____      |          /           _____                            || |                                     /           _____      |                                       /           _____ || |          /           _____                            |
|                                    /  119   9*\/ 181       |  ___    /  119   9*\/ 181                             || |                                    /  119   9*\/ 181       |                               ___    /  119   9*\/ 181  || |         /  119   9*\/ 181                             |
|                                 3 /   --- + ---------      |\/ 3 *3 /   --- + ---------                ___         || |                                 3 /   --- + ---------      |              ___            \/ 3 *3 /   --- + --------- || |      3 /   --- + ---------                            |
|  1              5               \/     2        2          |      \/     2        2                5*\/ 3          || |  1              5               \/     2        2          |          5*\/ 3                   \/     2        2     || |  1   \/     2        2                   5            |
|- - - ------------------------ + ---------------------- + I*|---------------------------- + ------------------------||*|- - - ------------------------ + ---------------------- + I*|- ------------------------ - ----------------------------||*|- - - ---------------------- + ------------------------|
|  3          _________________             6                |             6                        _________________|| |  3          _________________             6                |         _________________                6              || |  3             3                     _________________|
|            /           _____                               |                                     /           _____ || |            /           _____                               |        /           _____                                || |                                     /           _____ |
|           /  119   9*\/ 181                                |                                    /  119   9*\/ 181  || |           /  119   9*\/ 181                                |       /  119   9*\/ 181                                 || |                                    /  119   9*\/ 181  |
|      6*3 /   --- + ---------                               |                               6*3 /   --- + --------- || |      6*3 /   --- + ---------                               |  6*3 /   --- + ---------                                || |                               3*3 /   --- + --------- |
\        \/     2        2                                   \                                 \/     2        2     // \        \/     2        2                                   \    \/     2        2                                    // \                                 \/     2        2     /

$$\left(- \frac{1}{3} - \frac{5}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} + i \left(\frac{5 \sqrt{3}}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt{3} \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6}\right)\right) \left(- \frac{1}{3} - \frac{5}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}} + \frac{\sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{6} - \frac{5 \sqrt{3}}{6 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}\right)\right) \left(- \frac{\sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}{3} - \frac{1}{3} + \frac{5}{3 \sqrt[3]{\frac{119}{2} + \frac{9 \sqrt{181}}{2}}}\right)$$

-5

$$-5$$

-5

Respuesta numérica [src]

x1 = 0.319901002116328 + 1.71662807786013*i

x2 = 0.319901002116328 - 1.71662807786013*i

x3 = -1.63980200423266

x3 = -1.63980200423266

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Expresiones idénticas

Expresiones semejantes

X^3+x^2+2*x+5=0 la ecuación

Solución numérica:

Solución