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La ecuación:
Ecuación 2^2-x-1=x^2-5*x-(-1-x^2)
Ecuación (x-4)^2+(x+9)^2=2*x^2
Ecuación x^3-x^2-5=0
Ecuación (x-4)(x^2+16x+64)=13(x+8)
Expresar {x} en función de y en la ecuación:
18*x+19*y=7
10*x+5*y=-17
5*x-5*y=20
-13*x-6*y=13
Expresiones idénticas
x^ tres -x^ dos - cinco = cero
x al cubo menos x al cuadrado menos 5 es igual a 0
x en el grado tres menos x en el grado dos menos cinco es igual a cero
x3-x2-5=0
x³-x²-5=0
x en el grado 3-x en el grado 2-5=0
x^3-x^2-5=O
Expresiones semejantes
x^3-x^2+5=0
x^3+x^2-5=0

x^3-x^2-5=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3    2        
x  - x  - 5 = 0

\left(x^{3} - x^{2}\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 = 0

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} = 0

x_{1} x_{2} x_{3} = -5

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

              ________________                                /             ________________                           \
             /         ______                                 |            /         ______                            |
            /  137   \/ 2085                                  |    ___    /  137   \/ 2085                             |
         3 /   --- + --------                                 |  \/ 3 *3 /   --- + --------               ___          |
     1   \/     54      18                  1                 |        \/     54      18                \/ 3           |
x1 = - - --------------------- - ------------------------ + I*|- --------------------------- + ------------------------|
     3             2                     ________________     |               2                        ________________|
                                        /         ______      |                                       /         ______ |
                                       /  137   \/ 2085       |                                      /  137   \/ 2085  |
                                 18*3 /   --- + --------      |                                18*3 /   --- + -------- |
                                    \/     54      18         \                                   \/     54      18    /

x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} - \frac{1}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} + \frac{\sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}\right)

              ________________                                /           ________________                           \
             /         ______                                 |          /         ______                            |
            /  137   \/ 2085                                  |  ___    /  137   \/ 2085                             |
         3 /   --- + --------                                 |\/ 3 *3 /   --- + --------               ___          |
     1   \/     54      18                  1                 |      \/     54      18                \/ 3           |
x2 = - - --------------------- - ------------------------ + I*|--------------------------- - ------------------------|
     3             2                     ________________     |             2                        ________________|
                                        /         ______      |                                     /         ______ |
                                       /  137   \/ 2085       |                                    /  137   \/ 2085  |
                                 18*3 /   --- + --------      |                              18*3 /   --- + -------- |
                                    \/     54      18         \                                 \/     54      18    /

x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} - \frac{1}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2}\right)

              ________________                          
             /         ______                           
     1      /  137   \/ 2085                1           
x3 = - + 3 /   --- + --------  + -----------------------
     3   \/     54      18              ________________
                                       /         ______ 
                                      /  137   \/ 2085  
                                 9*3 /   --- + -------- 
                                   \/     54      18

x_{3} = \frac{1}{9 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{1}{3} + \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}

x3 = 1/(9*(sqrt(2085)/18 + 137/54)^(1/3)) + 1/3 + (sqrt(2085)/18 + 137/54)^(1/3)

Suma y producto de raíces [src]

suma

         ________________                                /             ________________                           \            ________________                                /           ________________                           \                                                      
        /         ______                                 |            /         ______                            |           /         ______                                 |          /         ______                            |                                                      
       /  137   \/ 2085                                  |    ___    /  137   \/ 2085                             |          /  137   \/ 2085                                  |  ___    /  137   \/ 2085                             |            ________________                          
    3 /   --- + --------                                 |  \/ 3 *3 /   --- + --------               ___          |       3 /   --- + --------                                 |\/ 3 *3 /   --- + --------               ___          |           /         ______                           
1   \/     54      18                  1                 |        \/     54      18                \/ 3           |   1   \/     54      18                  1                 |      \/     54      18                \/ 3           |   1      /  137   \/ 2085                1           
- - --------------------- - ------------------------ + I*|- --------------------------- + ------------------------| + - - --------------------- - ------------------------ + I*|--------------------------- - ------------------------| + - + 3 /   --- + --------  + -----------------------
3             2                     ________________     |               2                        ________________|   3             2                     ________________     |             2                        ________________|   3   \/     54      18              ________________
                                   /         ______      |                                       /         ______ |                                      /         ______      |                                     /         ______ |                                     /         ______ 
                                  /  137   \/ 2085       |                                      /  137   \/ 2085  |                                     /  137   \/ 2085       |                                    /  137   \/ 2085  |                                    /  137   \/ 2085  
                            18*3 /   --- + --------      |                                18*3 /   --- + -------- |                               18*3 /   --- + --------      |                              18*3 /   --- + -------- |                               9*3 /   --- + -------- 
                               \/     54      18         \                                   \/     54      18    /                                  \/     54      18         \                                 \/     54      18    /                                 \/     54      18

\left(\frac{1}{9 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{1}{3} + \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} - \frac{1}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} + \frac{\sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} - \frac{1}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2}\right)\right)\right)

      /           ________________                           \     /             ________________                           \
      |          /         ______                            |     |            /         ______                            |
      |  ___    /  137   \/ 2085                             |     |    ___    /  137   \/ 2085                             |
      |\/ 3 *3 /   --- + --------               ___          |     |  \/ 3 *3 /   --- + --------               ___          |
      |      \/     54      18                \/ 3           |     |        \/     54      18                \/ 3           |
1 + I*|--------------------------- - ------------------------| + I*|- --------------------------- + ------------------------|
      |             2                        ________________|     |               2                        ________________|
      |                                     /         ______ |     |                                       /         ______ |
      |                                    /  137   \/ 2085  |     |                                      /  137   \/ 2085  |
      |                              18*3 /   --- + -------- |     |                                18*3 /   --- + -------- |
      \                                 \/     54      18    /     \                                   \/     54      18    /

1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} + \frac{\sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}\right) + i \left(- \frac{\sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2}\right)

producto

/         ________________                                /             ________________                           \\ /         ________________                                /           ________________                           \\                                                      
|        /         ______                                 |            /         ______                            || |        /         ______                                 |          /         ______                            ||                                                      
|       /  137   \/ 2085                                  |    ___    /  137   \/ 2085                             || |       /  137   \/ 2085                                  |  ___    /  137   \/ 2085                             || /         ________________                          \
|    3 /   --- + --------                                 |  \/ 3 *3 /   --- + --------               ___          || |    3 /   --- + --------                                 |\/ 3 *3 /   --- + --------               ___          || |        /         ______                           |
|1   \/     54      18                  1                 |        \/     54      18                \/ 3           || |1   \/     54      18                  1                 |      \/     54      18                \/ 3           || |1      /  137   \/ 2085                1           |
|- - --------------------- - ------------------------ + I*|- --------------------------- + ------------------------||*|- - --------------------- - ------------------------ + I*|--------------------------- - ------------------------||*|- + 3 /   --- + --------  + -----------------------|
|3             2                     ________________     |               2                        ________________|| |3             2                     ________________     |             2                        ________________|| |3   \/     54      18              ________________|
|                                   /         ______      |                                       /         ______ || |                                   /         ______      |                                     /         ______ || |                                  /         ______ |
|                                  /  137   \/ 2085       |                                      /  137   \/ 2085  || |                                  /  137   \/ 2085       |                                    /  137   \/ 2085  || |                                 /  137   \/ 2085  |
|                            18*3 /   --- + --------      |                                18*3 /   --- + -------- || |                            18*3 /   --- + --------      |                              18*3 /   --- + -------- || |                            9*3 /   --- + -------- |
\                               \/     54      18         \                                   \/     54      18    // \                               \/     54      18         \                                 \/     54      18    // \                              \/     54      18    /

\left(- \frac{\sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} - \frac{1}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} - \frac{1}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}{2} + \frac{\sqrt{3}}{18 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}}\right)\right) \left(\frac{1}{9 \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}} + \frac{1}{3} + \sqrt[3]{\frac{\sqrt{2085}}{18} + \frac{137}{54}}\right)

5

Respuesta numérica [src]

x1 = -0.558171649312106 - 1.43213479425353*i

x2 = -0.558171649312106 + 1.43213479425353*i

x3 = 2.11634329862421

x3 = 2.11634329862421

Gráfico

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Expresiones idénticas

Expresiones semejantes

x^3-x^2-5=0 la ecuación

Solución numérica:

Solución