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La ecuación:
Ecuación x/3/7=9/14
Ecuación 25*x^2-1=0
Ecuación (x-2740)/20=360
Ecuación 2/3(1/3x-1/2)=4x+21/2
Expresar {x} en función de y en la ecuación:
19*x-5*y=12
-2*x+1*y=-8
6*x+8*y=0
19*x-1*y=2
Gráfico de la función y =:
x^3-6*x+2
Expresiones idénticas
x^ tres - seis *x+ dos = cero
x al cubo menos 6 multiplicar por x más 2 es igual a 0
x en el grado tres menos seis multiplicar por x más dos es igual a cero
x3-6*x+2=0
x³-6*x+2=0
x en el grado 3-6*x+2=0
x^3-6x+2=0
x3-6x+2=0
x^3-6*x+2=O
Expresiones semejantes
x^3-6*x-2=0
x^3+6*x+2=0

x^3-6*x+2=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3              
x  - 6*x + 2 = 0

\left(x^{3} - 6 x\right) + 2 = 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 = 0

q = \frac{c}{a}

q = -6

v = \frac{d}{a}

v = 2

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} = 0

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -6

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

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

                                                      /                                                        /    /  ___\\            /    /  ___\\\            /    /  ___\\            /    /  ___\\
                                                      |                                                 ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /||     ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /|
                                                      |                                               \/ 2 *sin|-----------|   \/ 6 *cos|-----------||   \/ 2 *cos|-----------|   \/ 6 *sin|-----------|
           /                 1                  \     |      /                 1                  \            \     3     /            \     3     /|            \     3     /            \     3     /
x1 = - 6*re|------------------------------------| + I*|- 6*im|------------------------------------| + ---------------------- + ----------------------| + ---------------------- - ----------------------
           |   _________________ /          ___\|     |      |   _________________ /          ___\|             2                        2           |             2                        2           
           |3 /             ___  |  1   I*\/ 3 ||     |      |3 /             ___  |  1   I*\/ 3 ||                                                  |                                                  
           |\/  27 + 27*I*\/ 7  *|- - - -------||     |      |\/  27 + 27*I*\/ 7  *|- - - -------||                                                  |                                                  
           \                     \  2      2   //     \      \                     \  2      2   //                                                  /

x_{1} = - \frac{\sqrt{6} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + \frac{\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + i \left(- 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + \frac{\sqrt{2} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{6} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2}\right)

                                                      /                                                        /    /  ___\\            /    /  ___\\\            /    /  ___\\            /    /  ___\\
                                                      |                                                 ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /||     ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /|
                                                      |                                               \/ 2 *sin|-----------|   \/ 6 *cos|-----------||   \/ 2 *cos|-----------|   \/ 6 *sin|-----------|
           /                 1                  \     |      /                 1                  \            \     3     /            \     3     /|            \     3     /            \     3     /
x2 = - 6*re|------------------------------------| + I*|- 6*im|------------------------------------| + ---------------------- - ----------------------| + ---------------------- + ----------------------
           |   _________________ /          ___\|     |      |   _________________ /          ___\|             2                        2           |             2                        2           
           |3 /             ___  |  1   I*\/ 3 ||     |      |3 /             ___  |  1   I*\/ 3 ||                                                  |                                                  
           |\/  27 + 27*I*\/ 7  *|- - + -------||     |      |\/  27 + 27*I*\/ 7  *|- - + -------||                                                  |                                                  
           \                     \  2      2   //     \      \                     \  2      2   //                                                  /

x_{2} = \frac{\sqrt{6} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + i \left(- \frac{\sqrt{6} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{2} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)}\right)

                                 _________________
                              3 /             ___ 
                6             \/  27 + 27*I*\/ 7  
x3 = - -------------------- - --------------------
          _________________            3          
       3 /             ___                        
       \/  27 + 27*I*\/ 7

x_{3} = - \frac{\sqrt[3]{27 + 27 \sqrt{7} i}}{3} - \frac{6}{\sqrt[3]{27 + 27 \sqrt{7} i}}

x3 = -(27 + 27*sqrt(7)*i)^(1/3)/3 - 6/(27 + 27*sqrt(7)*i)^(1/3)

Suma y producto de raíces [src]

suma

                                                 /                                                        /    /  ___\\            /    /  ___\\\            /    /  ___\\            /    /  ___\\                                                    /                                                        /    /  ___\\            /    /  ___\\\            /    /  ___\\            /    /  ___\\                                                
                                                 |                                                 ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /||     ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /|                                                    |                                                 ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /||     ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /|                               _________________
                                                 |                                               \/ 2 *sin|-----------|   \/ 6 *cos|-----------||   \/ 2 *cos|-----------|   \/ 6 *sin|-----------|                                                    |                                               \/ 2 *sin|-----------|   \/ 6 *cos|-----------||   \/ 2 *cos|-----------|   \/ 6 *sin|-----------|                            3 /             ___ 
      /                 1                  \     |      /                 1                  \            \     3     /            \     3     /|            \     3     /            \     3     /         /                 1                  \     |      /                 1                  \            \     3     /            \     3     /|            \     3     /            \     3     /              6             \/  27 + 27*I*\/ 7  
- 6*re|------------------------------------| + I*|- 6*im|------------------------------------| + ---------------------- + ----------------------| + ---------------------- - ---------------------- + - 6*re|------------------------------------| + I*|- 6*im|------------------------------------| + ---------------------- - ----------------------| + ---------------------- + ---------------------- + - -------------------- - --------------------
      |   _________________ /          ___\|     |      |   _________________ /          ___\|             2                        2           |             2                        2                    |   _________________ /          ___\|     |      |   _________________ /          ___\|             2                        2           |             2                        2                   _________________            3          
      |3 /             ___  |  1   I*\/ 3 ||     |      |3 /             ___  |  1   I*\/ 3 ||                                                  |                                                           |3 /             ___  |  1   I*\/ 3 ||     |      |3 /             ___  |  1   I*\/ 3 ||                                                  |                                                       3 /             ___                        
      |\/  27 + 27*I*\/ 7  *|- - - -------||     |      |\/  27 + 27*I*\/ 7  *|- - - -------||                                                  |                                                           |\/  27 + 27*I*\/ 7  *|- - + -------||     |      |\/  27 + 27*I*\/ 7  *|- - + -------||                                                  |                                                       \/  27 + 27*I*\/ 7                         
      \                     \  2      2   //     \      \                     \  2      2   //                                                  /                                                           \                     \  2      2   //     \      \                     \  2      2   //                                                  /

\left(\left(\frac{\sqrt{6} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + i \left(- \frac{\sqrt{6} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{2} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)}\right)\right) + \left(- \frac{\sqrt{6} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + \frac{\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + i \left(- 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + \frac{\sqrt{2} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{6} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2}\right)\right)\right) + \left(- \frac{\sqrt[3]{27 + 27 \sqrt{7} i}}{3} - \frac{6}{\sqrt[3]{27 + 27 \sqrt{7} i}}\right)

                                                                                                                                            /                                                        /    /  ___\\            /    /  ___\\\     /                                                        /    /  ___\\            /    /  ___\\\                         
                                                                                                                      _________________     |                                                 ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /||     |                                                 ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /||                         
                                                                                                                   3 /             ___      |                                               \/ 2 *sin|-----------|   \/ 6 *cos|-----------||     |                                               \/ 2 *sin|-----------|   \/ 6 *cos|-----------||            /    /  ___\\
           6                 /                 1                  \       /                 1                  \   \/  27 + 27*I*\/ 7       |      /                 1                  \            \     3     /            \     3     /|     |      /                 1                  \            \     3     /            \     3     /|     ___    |atan\\/ 7 /|
- -------------------- - 6*re|------------------------------------| - 6*re|------------------------------------| - -------------------- + I*|- 6*im|------------------------------------| + ---------------------- - ----------------------| + I*|- 6*im|------------------------------------| + ---------------------- + ----------------------| + \/ 2 *cos|-----------|
     _________________       |   _________________ /          ___\|       |   _________________ /          ___\|            3               |      |   _________________ /          ___\|             2                        2           |     |      |   _________________ /          ___\|             2                        2           |            \     3     /
  3 /             ___        |3 /             ___  |  1   I*\/ 3 ||       |3 /             ___  |  1   I*\/ 3 ||                            |      |3 /             ___  |  1   I*\/ 3 ||                                                  |     |      |3 /             ___  |  1   I*\/ 3 ||                                                  |                         
  \/  27 + 27*I*\/ 7         |\/  27 + 27*I*\/ 7  *|- - + -------||       |\/  27 + 27*I*\/ 7  *|- - - -------||                            |      |\/  27 + 27*I*\/ 7  *|- - + -------||                                                  |     |      |\/  27 + 27*I*\/ 7  *|- - - -------||                                                  |                         
                             \                     \  2      2   //       \                     \  2      2   //                            \      \                     \  2      2   //                                                  /     \      \                     \  2      2   //                                                  /

- 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} - 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + \sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)} - \frac{\sqrt[3]{27 + 27 \sqrt{7} i}}{3} + i \left(- 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + \frac{\sqrt{2} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{6} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2}\right) + i \left(- \frac{\sqrt{6} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{2} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)}\right) - \frac{6}{\sqrt[3]{27 + 27 \sqrt{7} i}}

producto

/                                                 /                                                        /    /  ___\\            /    /  ___\\\            /    /  ___\\            /    /  ___\\\ /                                                 /                                                        /    /  ___\\            /    /  ___\\\            /    /  ___\\            /    /  ___\\\                                                
|                                                 |                                                 ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /||     ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /|| |                                                 |                                                 ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /||     ___    |atan\\/ 7 /|     ___    |atan\\/ 7 /|| /                            _________________\
|                                                 |                                               \/ 2 *sin|-----------|   \/ 6 *cos|-----------||   \/ 2 *cos|-----------|   \/ 6 *sin|-----------|| |                                                 |                                               \/ 2 *sin|-----------|   \/ 6 *cos|-----------||   \/ 2 *cos|-----------|   \/ 6 *sin|-----------|| |                         3 /             ___ |
|      /                 1                  \     |      /                 1                  \            \     3     /            \     3     /|            \     3     /            \     3     /| |      /                 1                  \     |      /                 1                  \            \     3     /            \     3     /|            \     3     /            \     3     /| |           6             \/  27 + 27*I*\/ 7  |
|- 6*re|------------------------------------| + I*|- 6*im|------------------------------------| + ---------------------- + ----------------------| + ---------------------- - ----------------------|*|- 6*re|------------------------------------| + I*|- 6*im|------------------------------------| + ---------------------- - ----------------------| + ---------------------- + ----------------------|*|- -------------------- - --------------------|
|      |   _________________ /          ___\|     |      |   _________________ /          ___\|             2                        2           |             2                        2           | |      |   _________________ /          ___\|     |      |   _________________ /          ___\|             2                        2           |             2                        2           | |     _________________            3          |
|      |3 /             ___  |  1   I*\/ 3 ||     |      |3 /             ___  |  1   I*\/ 3 ||                                                  |                                                  | |      |3 /             ___  |  1   I*\/ 3 ||     |      |3 /             ___  |  1   I*\/ 3 ||                                                  |                                                  | |  3 /             ___                        |
|      |\/  27 + 27*I*\/ 7  *|- - - -------||     |      |\/  27 + 27*I*\/ 7  *|- - - -------||                                                  |                                                  | |      |\/  27 + 27*I*\/ 7  *|- - + -------||     |      |\/  27 + 27*I*\/ 7  *|- - + -------||                                                  |                                                  | \  \/  27 + 27*I*\/ 7                         /
\      \                     \  2      2   //     \      \                     \  2      2   //                                                  /                                                  / \      \                     \  2      2   //     \      \                     \  2      2   //                                                  /                                                  /

\left(- \frac{\sqrt{6} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + \frac{\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + i \left(- 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + \frac{\sqrt{2} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{6} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2}\right)\right) \left(\frac{\sqrt{6} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{2} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)} + i \left(- \frac{\sqrt{6} \cos{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} + \frac{\sqrt{2} \sin{\left(\frac{\operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}}{2} - 6 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{27 + 27 \sqrt{7} i}}\right)}\right)\right) \left(- \frac{\sqrt[3]{27 + 27 \sqrt{7} i}}{3} - \frac{6}{\sqrt[3]{27 + 27 \sqrt{7} i}}\right)

  /         /      /  ___\\\ /                 2/3\
  |         |2*atan\\/ 7 /|| |    /        ___\   |
2*|1 - 2*cos|-------------||*\2 + \1 + I*\/ 7 /   /
  \         \      3      //                       
---------------------------------------------------
                     _____________                 
                  3 /         ___                  
                  \/  1 + I*\/ 7

\frac{2 \left(1 - 2 \cos{\left(\frac{2 \operatorname{atan}{\left(\sqrt{7} \right)}}{3} \right)}\right) \left(2 + \left(1 + \sqrt{7} i\right)^{\frac{2}{3}}\right)}{\sqrt[3]{1 + \sqrt{7} i}}

2*(1 - 2*cos(2*atan(sqrt(7))/3))*(2 + (1 + i*sqrt(7))^(2/3))/(1 + i*sqrt(7))^(1/3)

Respuesta numérica [src]

x1 = 2.26180224525997

x2 = -2.60167913188315

x3 = 0.339876886623183

x3 = 0.339876886623183

Gráfico

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Expresiones idénticas

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x^3-6*x+2=0 la ecuación

Solución numérica:

Solución