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La ecuación:
Ecuación x^4+2*x^2-8=0
Ecuación x-y=1
Ecuación z^2+3+4*i=0
Ecuación x^2-4x+5=0
Expresar {x} en función de y en la ecuación:
-15*x+17*y=13
4*x-7*y=4
-14*x+10*y=19
1*x+6*y=6
Expresiones idénticas
x^ tres -5x^ dos -9x- cuarenta y cinco = cero
x al cubo menos 5x al cuadrado menos 9x menos 45 es igual a 0
x en el grado tres menos 5x en el grado dos menos 9x menos cuarenta y cinco es igual a cero
x3-5x2-9x-45=0
x³-5x²-9x-45=0
x en el grado 3-5x en el grado 2-9x-45=0
x^3-5x^2-9x-45=O
Expresiones semejantes
x^3-5x^2-9x+45=0
x^3-5x^2+9x-45=0
x^3+5x^2-9x-45=0

x^3-5x^2-9x-45=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3      2               
x  - 5*x  - 9*x - 45 = 0

\left(- 9 x + \left(x^{3} - 5 x^{2}\right)\right) - 45 = 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 = -5

q = \frac{c}{a}

q = -9

v = \frac{d}{a}

v = -45

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} = 5

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

x_{1} x_{2} x_{3} = -45

Respuesta rápida [src]

                                        ________________     /             ________________                          \
                                       /         ______      |            /         ______                           |
                                      /  935   \/ 9057       |    ___    /  935   \/ 9057                            |
                                   3 /   --- + --------      |  \/ 3 *3 /   --- + --------                 ___       |
     5              26             \/     27      3          |        \/     27      3                26*\/ 3        |
x1 = - - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------|
     3          ________________             2               |               2                       ________________|
               /         ______                              |                                      /         ______ |
              /  935   \/ 9057                               |                                     /  935   \/ 9057  |
         9*3 /   --- + --------                              |                                9*3 /   --- + -------- |
           \/     27      3                                  \                                  \/     27      3     /

x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} - \frac{26}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{5}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} + \frac{26 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}\right)

                                        ________________     /           ________________                          \
                                       /         ______      |          /         ______                           |
                                      /  935   \/ 9057       |  ___    /  935   \/ 9057                            |
                                   3 /   --- + --------      |\/ 3 *3 /   --- + --------                 ___       |
     5              26             \/     27      3          |      \/     27      3                26*\/ 3        |
x2 = - - ----------------------- - --------------------- + I*|--------------------------- - -----------------------|
     3          ________________             2               |             2                       ________________|
               /         ______                              |                                    /         ______ |
              /  935   \/ 9057                               |                                   /  935   \/ 9057  |
         9*3 /   --- + --------                              |                              9*3 /   --- + -------- |
           \/     27      3                                  \                                \/     27      3     /

x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} - \frac{26}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{5}{3} + i \left(- \frac{26 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2}\right)

              ________________                          
             /         ______                           
     5      /  935   \/ 9057                52          
x3 = - + 3 /   --- + --------  + -----------------------
     3   \/     27      3               ________________
                                       /         ______ 
                                      /  935   \/ 9057  
                                 9*3 /   --- + -------- 
                                   \/     27      3

x_{3} = \frac{52}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{5}{3} + \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}

x3 = 52/(9*(sqrt(9057)/3 + 935/27)^(1/3)) + 5/3 + (sqrt(9057)/3 + 935/27)^(1/3)

Suma y producto de raíces [src]

suma

                                   ________________     /             ________________                          \                                      ________________     /           ________________                          \                                                      
                                  /         ______      |            /         ______                           |                                     /         ______      |          /         ______                           |                                                      
                                 /  935   \/ 9057       |    ___    /  935   \/ 9057                            |                                    /  935   \/ 9057       |  ___    /  935   \/ 9057                            |            ________________                          
                              3 /   --- + --------      |  \/ 3 *3 /   --- + --------                 ___       |                                 3 /   --- + --------      |\/ 3 *3 /   --- + --------                 ___       |           /         ______                           
5              26             \/     27      3          |        \/     27      3                26*\/ 3        |   5              26             \/     27      3          |      \/     27      3                26*\/ 3        |   5      /  935   \/ 9057                52          
- - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------| + - - ----------------------- - --------------------- + I*|--------------------------- - -----------------------| + - + 3 /   --- + --------  + -----------------------
3          ________________             2               |               2                       ________________|   3          ________________             2               |             2                       ________________|   3   \/     27      3               ________________
          /         ______                              |                                      /         ______ |             /         ______                              |                                    /         ______ |                                     /         ______ 
         /  935   \/ 9057                               |                                     /  935   \/ 9057  |            /  935   \/ 9057                               |                                   /  935   \/ 9057  |                                    /  935   \/ 9057  
    9*3 /   --- + --------                              |                                9*3 /   --- + -------- |       9*3 /   --- + --------                              |                              9*3 /   --- + -------- |                               9*3 /   --- + -------- 
      \/     27      3                                  \                                  \/     27      3     /         \/     27      3                                  \                                \/     27      3     /                                 \/     27      3

\left(\frac{52}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{5}{3} + \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} - \frac{26}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{5}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} + \frac{26 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} - \frac{26}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{5}{3} + i \left(- \frac{26 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2}\right)\right)\right)

      /           ________________                          \     /             ________________                          \
      |          /         ______                           |     |            /         ______                           |
      |  ___    /  935   \/ 9057                            |     |    ___    /  935   \/ 9057                            |
      |\/ 3 *3 /   --- + --------                 ___       |     |  \/ 3 *3 /   --- + --------                 ___       |
      |      \/     27      3                26*\/ 3        |     |        \/     27      3                26*\/ 3        |
5 + I*|--------------------------- - -----------------------| + I*|- --------------------------- + -----------------------|
      |             2                       ________________|     |               2                       ________________|
      |                                    /         ______ |     |                                      /         ______ |
      |                                   /  935   \/ 9057  |     |                                     /  935   \/ 9057  |
      |                              9*3 /   --- + -------- |     |                                9*3 /   --- + -------- |
      \                                \/     27      3     /     \                                  \/     27      3     /

5 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} + \frac{26 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}\right) + i \left(- \frac{26 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2}\right)

producto

/                                   ________________     /             ________________                          \\ /                                   ________________     /           ________________                          \\                                                      
|                                  /         ______      |            /         ______                           || |                                  /         ______      |          /         ______                           ||                                                      
|                                 /  935   \/ 9057       |    ___    /  935   \/ 9057                            || |                                 /  935   \/ 9057       |  ___    /  935   \/ 9057                            || /         ________________                          \
|                              3 /   --- + --------      |  \/ 3 *3 /   --- + --------                 ___       || |                              3 /   --- + --------      |\/ 3 *3 /   --- + --------                 ___       || |        /         ______                           |
|5              26             \/     27      3          |        \/     27      3                26*\/ 3        || |5              26             \/     27      3          |      \/     27      3                26*\/ 3        || |5      /  935   \/ 9057                52          |
|- - ----------------------- - --------------------- + I*|- --------------------------- + -----------------------||*|- - ----------------------- - --------------------- + I*|--------------------------- - -----------------------||*|- + 3 /   --- + --------  + -----------------------|
|3          ________________             2               |               2                       ________________|| |3          ________________             2               |             2                       ________________|| |3   \/     27      3               ________________|
|          /         ______                              |                                      /         ______ || |          /         ______                              |                                    /         ______ || |                                  /         ______ |
|         /  935   \/ 9057                               |                                     /  935   \/ 9057  || |         /  935   \/ 9057                               |                                   /  935   \/ 9057  || |                                 /  935   \/ 9057  |
|    9*3 /   --- + --------                              |                                9*3 /   --- + -------- || |    9*3 /   --- + --------                              |                              9*3 /   --- + -------- || |                            9*3 /   --- + -------- |
\      \/     27      3                                  \                                  \/     27      3     // \      \/     27      3                                  \                                \/     27      3     // \                              \/     27      3     /

\left(- \frac{\sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} - \frac{26}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{5}{3} + i \left(- \frac{26 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} - \frac{26}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{5}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}{2} + \frac{26 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}}\right)\right) \left(\frac{52}{9 \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}} + \frac{5}{3} + \sqrt[3]{\frac{\sqrt{9057}}{3} + \frac{935}{27}}\right)

45

Respuesta numérica [src]

x1 = -1.07112748277456 + 2.27006984051383*i

x2 = 7.14225496554912

x3 = -1.07112748277456 - 2.27006984051383*i

x3 = -1.07112748277456 - 2.27006984051383*i

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Expresiones idénticas

Expresiones semejantes

x^3-5x^2-9x-45=0 la ecuación

Solución numérica:

Solución