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La ecuación:
Ecuación x^2+3x=4
Ecuación -24-y=-16
Ecuación (11x+14)-(5x-8)=25
Ecuación 4(x-6)=x-9
Expresar {x} en función de y en la ecuación:
-18*x+8*y=-2
15*x+1*y=19
-3*x+17*y=-4
-14*x-12*y=5
Gráfico de la función y =:
x^3-x^2-x-1
Expresiones idénticas
x^ tres -x^ dos -x- uno = cero
x al cubo menos x al cuadrado menos x menos 1 es igual a 0
x en el grado tres menos x en el grado dos menos x menos uno es igual a cero
x3-x2-x-1=0
x³-x²-x-1=0
x en el grado 3-x en el grado 2-x-1=0
x^3-x^2-x-1=O
Expresiones semejantes
x^3-x^2+x-1=0
x^3-x^2-x+1=0
x^3+x^2-x-1=0

x^3-x^2-x-1=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3    2            
x  - x  - x - 1 = 0

\left(- x + \left(x^{3} - x^{2}\right)\right) - 1 = 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 = -1

v = \frac{d}{a}

v = -1

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} = -1

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

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

                                _____________     /             _____________                       \                                   _____________     /           _____________                       \                                                
                               /        ____      |            /        ____                        |                                  /        ____      |          /        ____                        |                                                
                              /  19   \/ 33       |    ___    /  19   \/ 33                         |                                 /  19   \/ 33       |  ___    /  19   \/ 33                         |            _____________                       
                           3 /   -- + ------      |  \/ 3 *3 /   -- + ------              ___       |                              3 /   -- + ------      |\/ 3 *3 /   -- + ------              ___       |           /        ____                        
1            2             \/    27     9         |        \/    27     9             2*\/ 3        |   1            2             \/    27     9         |      \/    27     9             2*\/ 3        |   1      /  19   \/ 33              4          
- - -------------------- - ------------------ + I*|- ------------------------ + --------------------| + - - -------------------- - ------------------ + I*|------------------------ - --------------------| + - + 3 /   -- + ------  + --------------------
3          _____________           2              |             2                      _____________|   3          _____________           2              |           2                      _____________|   3   \/    27     9              _____________
          /        ____                           |                                   /        ____ |             /        ____                           |                                 /        ____ |                                  /        ____ 
         /  19   \/ 33                            |                                  /  19   \/ 33  |            /  19   \/ 33                            |                                /  19   \/ 33  |                                 /  19   \/ 33  
    9*3 /   -- + ------                           |                             9*3 /   -- + ------ |       9*3 /   -- + ------                           |                           9*3 /   -- + ------ |                            9*3 /   -- + ------ 
      \/    27     9                              \                               \/    27     9    /         \/    27     9                              \                             \/    27     9    /                              \/    27     9

\left(\frac{1}{3} + \frac{4}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2}\right)\right)\right)

      /           _____________                       \     /             _____________                       \
      |          /        ____                        |     |            /        ____                        |
      |  ___    /  19   \/ 33                         |     |    ___    /  19   \/ 33                         |
      |\/ 3 *3 /   -- + ------              ___       |     |  \/ 3 *3 /   -- + ------              ___       |
      |      \/    27     9             2*\/ 3        |     |        \/    27     9             2*\/ 3        |
1 + I*|------------------------ - --------------------| + I*|- ------------------------ + --------------------|
      |           2                      _____________|     |             2                      _____________|
      |                                 /        ____ |     |                                   /        ____ |
      |                                /  19   \/ 33  |     |                                  /  19   \/ 33  |
      |                           9*3 /   -- + ------ |     |                             9*3 /   -- + ------ |
      \                             \/    27     9    /     \                               \/    27     9    /

1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}\right) + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2}\right)

producto

/                                _____________     /             _____________                       \\ /                                _____________     /           _____________                       \\                                                
|                               /        ____      |            /        ____                        || |                               /        ____      |          /        ____                        ||                                                
|                              /  19   \/ 33       |    ___    /  19   \/ 33                         || |                              /  19   \/ 33       |  ___    /  19   \/ 33                         || /         _____________                       \
|                           3 /   -- + ------      |  \/ 3 *3 /   -- + ------              ___       || |                           3 /   -- + ------      |\/ 3 *3 /   -- + ------              ___       || |        /        ____                        |
|1            2             \/    27     9         |        \/    27     9             2*\/ 3        || |1            2             \/    27     9         |      \/    27     9             2*\/ 3        || |1      /  19   \/ 33              4          |
|- - -------------------- - ------------------ + I*|- ------------------------ + --------------------||*|- - -------------------- - ------------------ + I*|------------------------ - --------------------||*|- + 3 /   -- + ------  + --------------------|
|3          _____________           2              |             2                      _____________|| |3          _____________           2              |           2                      _____________|| |3   \/    27     9              _____________|
|          /        ____                           |                                   /        ____ || |          /        ____                           |                                 /        ____ || |                               /        ____ |
|         /  19   \/ 33                            |                                  /  19   \/ 33  || |         /  19   \/ 33                            |                                /  19   \/ 33  || |                              /  19   \/ 33  |
|    9*3 /   -- + ------                           |                             9*3 /   -- + ------ || |    9*3 /   -- + ------                           |                           9*3 /   -- + ------ || |                         9*3 /   -- + ------ |
\      \/    27     9                              \                               \/    27     9    // \      \/    27     9                              \                             \/    27     9    // \                           \/    27     9    /

\left(- \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}\right)\right) \left(\frac{1}{3} + \frac{4}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}\right)

1

Respuesta rápida [src]

                                     _____________     /             _____________                       \
                                    /        ____      |            /        ____                        |
                                   /  19   \/ 33       |    ___    /  19   \/ 33                         |
                                3 /   -- + ------      |  \/ 3 *3 /   -- + ------              ___       |
     1            2             \/    27     9         |        \/    27     9             2*\/ 3        |
x1 = - - -------------------- - ------------------ + I*|- ------------------------ + --------------------|
     3          _____________           2              |             2                      _____________|
               /        ____                           |                                   /        ____ |
              /  19   \/ 33                            |                                  /  19   \/ 33  |
         9*3 /   -- + ------                           |                             9*3 /   -- + ------ |
           \/    27     9                              \                               \/    27     9    /

x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} + \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}\right)

                                     _____________     /           _____________                       \
                                    /        ____      |          /        ____                        |
                                   /  19   \/ 33       |  ___    /  19   \/ 33                         |
                                3 /   -- + ------      |\/ 3 *3 /   -- + ------              ___       |
     1            2             \/    27     9         |      \/    27     9             2*\/ 3        |
x2 = - - -------------------- - ------------------ + I*|------------------------ - --------------------|
     3          _____________           2              |           2                      _____________|
               /        ____                           |                                 /        ____ |
              /  19   \/ 33                            |                                /  19   \/ 33  |
         9*3 /   -- + ------                           |                           9*3 /   -- + ------ |
           \/    27     9                              \                             \/    27     9    /

x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2} - \frac{2}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{1}{3} + i \left(- \frac{2 \sqrt{3}}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}}{2}\right)

              _____________                       
             /        ____                        
     1      /  19   \/ 33              4          
x3 = - + 3 /   -- + ------  + --------------------
     3   \/    27     9              _____________
                                    /        ____ 
                                   /  19   \/ 33  
                              9*3 /   -- + ------ 
                                \/    27     9

x_{3} = \frac{1}{3} + \frac{4}{9 \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}} + \sqrt[3]{\frac{\sqrt{33}}{9} + \frac{19}{27}}

x3 = 1/3 + 4/(9*(sqrt(33)/9 + 19/27)^(1/3)) + (sqrt(33)/9 + 19/27)^(1/3)

Respuesta numérica [src]

x1 = -0.419643377607081 - 0.606290729207199*i

x2 = 1.83928675521416

x3 = -0.419643377607081 + 0.606290729207199*i

x3 = -0.419643377607081 + 0.606290729207199*i

Gráfico

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Expresiones idénticas

Expresiones semejantes

x^3-x^2-x-1=0 la ecuación

Solución numérica:

Solución