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La ecuación:
Ecuación x^4=(4x-21)^2
Ecuación (x+2)/9=(x-3)/2
Ecuación 1-2(5+3x)=15
Ecuación 2*x+2=-3
Expresar {x} en función de y en la ecuación:
-9*x-4*y=-20
12*x-14*y=20
5*x-13*y=17
-16*x+14*y=-9
Expresiones idénticas
x^ tres + dos x^2+9x- dieciocho = cero
x al cubo más 2x al cuadrado más 9x menos 18 es igual a 0
x en el grado tres más dos x al cuadrado más 9x menos dieciocho es igual a cero
x3+2x2+9x-18=0
x³+2x²+9x-18=0
x en el grado 3+2x en el grado 2+9x-18=0
x^3+2x^2+9x-18=O
Expresiones semejantes
x^3+2x^2+9x+18=0
x^3+2x^2-9x-18=0
x^3-2x^2+9x-18=0

x^3+2x^2+9x-18=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3      2               
x  + 2*x  + 9*x - 18 = 0

\left(9 x + \left(x^{3} + 2 x^{2}\right)\right) - 18 = 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 = 2

q = \frac{c}{a}

q = 9

v = \frac{d}{a}

v = -18

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} = -2

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 9

x_{1} x_{2} x_{3} = -18

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

                ________________                                /                                        ________________\
               /         ______                                 |                                       /         ______ |
              /  316   \/ 1383                                  |                               ___    /  316   \/ 1383  |
           3 /   --- + --------                                 |               ___           \/ 3 *3 /   --- + -------- |
       2   \/     27      3                   23                |          23*\/ 3                  \/     27      3     |
x1 = - - - --------------------- + ------------------------ + I*|- ------------------------ - ---------------------------|
       3             2                     ________________     |          ________________                2             |
                                          /         ______      |         /         ______                               |
                                         /  316   \/ 1383       |        /  316   \/ 1383                                |
                                   18*3 /   --- + --------      |  18*3 /   --- + --------                               |
                                      \/     27      3          \     \/     27      3                                   /

x_{1} = - \frac{\sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{2}{3} + \frac{23}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{23 \sqrt{3}}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}\right)

                ________________                                /           ________________                           \
               /         ______                                 |          /         ______                            |
              /  316   \/ 1383                                  |  ___    /  316   \/ 1383                             |
           3 /   --- + --------                                 |\/ 3 *3 /   --- + --------                 ___        |
       2   \/     27      3                   23                |      \/     27      3                23*\/ 3         |
x2 = - - - --------------------- + ------------------------ + I*|--------------------------- + ------------------------|
       3             2                     ________________     |             2                        ________________|
                                          /         ______      |                                     /         ______ |
                                         /  316   \/ 1383       |                                    /  316   \/ 1383  |
                                   18*3 /   --- + --------      |                              18*3 /   --- + -------- |
                                      \/     27      3          \                                 \/     27      3     /

x_{2} = - \frac{\sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{2}{3} + \frac{23}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + i \left(\frac{23 \sqrt{3}}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + \frac{\sqrt{3} \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2}\right)

                ________________                          
               /         ______                           
       2      /  316   \/ 1383                23          
x3 = - - + 3 /   --- + --------  - -----------------------
       3   \/     27      3               ________________
                                         /         ______ 
                                        /  316   \/ 1383  
                                   9*3 /   --- + -------- 
                                     \/     27      3

x_{3} = - \frac{23}{9 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} - \frac{2}{3} + \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}

x3 = -23/(9*(316/27 + sqrt(1383)/3)^(1/3)) - 2/3 + (316/27 + sqrt(1383)/3)^(1/3)

Suma y producto de raíces [src]

suma

           ________________                                /                                        ________________\              ________________                                /           ________________                           \                                                        
          /         ______                                 |                                       /         ______ |             /         ______                                 |          /         ______                            |                                                        
         /  316   \/ 1383                                  |                               ___    /  316   \/ 1383  |            /  316   \/ 1383                                  |  ___    /  316   \/ 1383                             |              ________________                          
      3 /   --- + --------                                 |               ___           \/ 3 *3 /   --- + -------- |         3 /   --- + --------                                 |\/ 3 *3 /   --- + --------                 ___        |             /         ______                           
  2   \/     27      3                   23                |          23*\/ 3                  \/     27      3     |     2   \/     27      3                   23                |      \/     27      3                23*\/ 3         |     2      /  316   \/ 1383                23          
- - - --------------------- + ------------------------ + I*|- ------------------------ - ---------------------------| + - - - --------------------- + ------------------------ + I*|--------------------------- + ------------------------| + - - + 3 /   --- + --------  - -----------------------
  3             2                     ________________     |          ________________                2             |     3             2                     ________________     |             2                        ________________|     3   \/     27      3               ________________
                                     /         ______      |         /         ______                               |                                        /         ______      |                                     /         ______ |                                       /         ______ 
                                    /  316   \/ 1383       |        /  316   \/ 1383                                |                                       /  316   \/ 1383       |                                    /  316   \/ 1383  |                                      /  316   \/ 1383  
                              18*3 /   --- + --------      |  18*3 /   --- + --------                               |                                 18*3 /   --- + --------      |                              18*3 /   --- + -------- |                                 9*3 /   --- + -------- 
                                 \/     27      3          \     \/     27      3                                   /                                    \/     27      3          \                                 \/     27      3     /                                   \/     27      3

\left(- \frac{23}{9 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} - \frac{2}{3} + \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{2}{3} + \frac{23}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{23 \sqrt{3}}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{2}{3} + \frac{23}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + i \left(\frac{23 \sqrt{3}}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + \frac{\sqrt{3} \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2}\right)\right)\right)

       /           ________________                           \     /                                        ________________\
       |          /         ______                            |     |                                       /         ______ |
       |  ___    /  316   \/ 1383                             |     |                               ___    /  316   \/ 1383  |
       |\/ 3 *3 /   --- + --------                 ___        |     |               ___           \/ 3 *3 /   --- + -------- |
       |      \/     27      3                23*\/ 3         |     |          23*\/ 3                  \/     27      3     |
-2 + I*|--------------------------- + ------------------------| + I*|- ------------------------ - ---------------------------|
       |             2                        ________________|     |          ________________                2             |
       |                                     /         ______ |     |         /         ______                               |
       |                                    /  316   \/ 1383  |     |        /  316   \/ 1383                                |
       |                              18*3 /   --- + -------- |     |  18*3 /   --- + --------                               |
       \                                 \/     27      3     /     \     \/     27      3                                   /

-2 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{23 \sqrt{3}}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}\right) + i \left(\frac{23 \sqrt{3}}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + \frac{\sqrt{3} \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2}\right)

producto

/           ________________                                /                                        ________________\\ /           ________________                                /           ________________                           \\                                                        
|          /         ______                                 |                                       /         ______ || |          /         ______                                 |          /         ______                            ||                                                        
|         /  316   \/ 1383                                  |                               ___    /  316   \/ 1383  || |         /  316   \/ 1383                                  |  ___    /  316   \/ 1383                             || /           ________________                          \
|      3 /   --- + --------                                 |               ___           \/ 3 *3 /   --- + -------- || |      3 /   --- + --------                                 |\/ 3 *3 /   --- + --------                 ___        || |          /         ______                           |
|  2   \/     27      3                   23                |          23*\/ 3                  \/     27      3     || |  2   \/     27      3                   23                |      \/     27      3                23*\/ 3         || |  2      /  316   \/ 1383                23          |
|- - - --------------------- + ------------------------ + I*|- ------------------------ - ---------------------------||*|- - - --------------------- + ------------------------ + I*|--------------------------- + ------------------------||*|- - + 3 /   --- + --------  - -----------------------|
|  3             2                     ________________     |          ________________                2             || |  3             2                     ________________     |             2                        ________________|| |  3   \/     27      3               ________________|
|                                     /         ______      |         /         ______                               || |                                     /         ______      |                                     /         ______ || |                                    /         ______ |
|                                    /  316   \/ 1383       |        /  316   \/ 1383                                || |                                    /  316   \/ 1383       |                                    /  316   \/ 1383  || |                                   /  316   \/ 1383  |
|                              18*3 /   --- + --------      |  18*3 /   --- + --------                               || |                              18*3 /   --- + --------      |                              18*3 /   --- + -------- || |                              9*3 /   --- + -------- |
\                                 \/     27      3          \     \/     27      3                                   // \                                 \/     27      3          \                                 \/     27      3     // \                                \/     27      3     /

\left(- \frac{\sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{2}{3} + \frac{23}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + i \left(\frac{23 \sqrt{3}}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + \frac{\sqrt{3} \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{2}{3} + \frac{23}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}{2} - \frac{23 \sqrt{3}}{18 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}}\right)\right) \left(- \frac{23}{9 \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}} - \frac{2}{3} + \sqrt[3]{\frac{316}{27} + \frac{\sqrt{1383}}{3}}\right)

18

Respuesta numérica [src]

x1 = -1.66854774542557 + 3.26771537233461*i

x2 = -1.66854774542557 - 3.26771537233461*i

x3 = 1.33709549085113

x3 = 1.33709549085113

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¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

x^3+2x^2+9x-18=0 la ecuación

Solución numérica:

Solución