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La ecuación:
Ecuación |x^2-1|-|x-3|=7
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
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
Gráfico de la función y =:
x^3-3*x^2+1
Expresiones idénticas
x^ tres - tres *x^ dos + uno = cero
x al cubo menos 3 multiplicar por x al cuadrado más 1 es igual a 0
x en el grado tres menos tres multiplicar por x en el grado dos más uno es igual a cero
x3-3*x2+1=0
x³-3*x²+1=0
x en el grado 3-3*x en el grado 2+1=0
x^3-3x^2+1=0
x3-3x2+1=0
x^3-3*x^2+1=O
Expresiones semejantes
x^3-3*x^2-1=0
x^3+3*x^2+1=0

x^3-3*x^2+1=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 3      2        
x  - 3*x  + 1 = 0

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

q = \frac{c}{a}

q = 0

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} = 3

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 0

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

       /pi\     /     /pi\     ___    /pi\                                         \     ___    /pi\                                                   /pi\     /     /pi\     ___    /pi\                                         \     ___    /pi\                                                                          _____________
    cos|--|     |  sin|--|   \/ 3 *cos|--|                                         |   \/ 3 *sin|--|                                                cos|--|     |  sin|--|   \/ 3 *cos|--|                                         |   \/ 3 *sin|--|                                                                         /         ___ 
       \9 /     |     \9 /            \9 /     /                1                 \|            \9 /     /                1                 \          \9 /     |     \9 /            \9 /     /                1                 \|            \9 /     /                1                 \               1               /  1   I*\/ 3  
1 - ------- + I*|- ------- - ------------- + im|----------------------------------|| + ------------- + re|----------------------------------| + 1 - ------- + I*|- ------- + ------------- + im|----------------------------------|| - ------------- + re|----------------------------------| + 1 + ------------------ + 3 /   - + ------- 
       2        |     2            2           |     _____________                ||         2           |     _____________                |          2        |     2            2           |     _____________                ||         2           |     _____________                |            _____________   \/    2      2    
                |                              |    /         ___  /          ___\||                     |    /         ___  /          ___\|                   |                              |    /         ___  /          ___\||                     |    /         ___  /          ___\|           /         ___                      
                |                              |   /  1   I*\/ 3   |  1   I*\/ 3 |||                     |   /  1   I*\/ 3   |  1   I*\/ 3 ||                   |                              |   /  1   I*\/ 3   |  1   I*\/ 3 |||                     |   /  1   I*\/ 3   |  1   I*\/ 3 ||          /  1   I*\/ 3                       
                |                              |3 /   - + ------- *|- - - -------|||                     |3 /   - + ------- *|- - - -------||                   |                              |3 /   - + ------- *|- - + -------|||                     |3 /   - + ------- *|- - + -------||       3 /   - + -------                      
                \                              \\/    2      2     \  2      2   ///                     \\/    2      2     \  2      2   //                   \                              \\/    2      2     \  2      2   ///                     \\/    2      2     \  2      2   //       \/    2      2

\left(\left(\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} - \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + 1 + i \left(\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} - \frac{\sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} \cos{\left(\frac{\pi}{9} \right)}}{2}\right)\right) + \left(- \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} + \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} + \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + 1 + i \left(- \frac{\sqrt{3} \cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sin{\left(\frac{\pi}{9} \right)}}{2} + \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)}\right)\right)\right) + \left(1 + \frac{1}{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}} + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}\right)

                              _____________               /     /pi\     ___    /pi\                                         \     /     /pi\     ___    /pi\                                         \                                                                                  
                             /         ___                |  sin|--|   \/ 3 *cos|--|                                         |     |  sin|--|   \/ 3 *cos|--|                                         |                                                                                  
            1               /  1   I*\/ 3        /pi\     |     \9 /            \9 /     /                1                 \|     |     \9 /            \9 /     /                1                 \|     /                1                 \     /                1                 \
3 + ------------------ + 3 /   - + -------  - cos|--| + I*|- ------- + ------------- + im|----------------------------------|| + I*|- ------- - ------------- + im|----------------------------------|| + re|----------------------------------| + re|----------------------------------|
         _____________   \/    2      2          \9 /     |     2            2           |     _____________                ||     |     2            2           |     _____________                ||     |     _____________                |     |     _____________                |
        /         ___                                     |                              |    /         ___  /          ___\||     |                              |    /         ___  /          ___\||     |    /         ___  /          ___\|     |    /         ___  /          ___\|
       /  1   I*\/ 3                                      |                              |   /  1   I*\/ 3   |  1   I*\/ 3 |||     |                              |   /  1   I*\/ 3   |  1   I*\/ 3 |||     |   /  1   I*\/ 3   |  1   I*\/ 3 ||     |   /  1   I*\/ 3   |  1   I*\/ 3 ||
    3 /   - + -------                                     |                              |3 /   - + ------- *|- - + -------|||     |                              |3 /   - + ------- *|- - - -------|||     |3 /   - + ------- *|- - + -------||     |3 /   - + ------- *|- - - -------||
    \/    2      2                                        \                              \\/    2      2     \  2      2   ///     \                              \\/    2      2     \  2      2   ///     \\/    2      2     \  2      2   //     \\/    2      2     \  2      2   //

- \cos{\left(\frac{\pi}{9} \right)} + \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} + \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} + 3 + \frac{1}{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}} + i \left(\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} - \frac{\sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} \cos{\left(\frac{\pi}{9} \right)}}{2}\right) + i \left(- \frac{\sqrt{3} \cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sin{\left(\frac{\pi}{9} \right)}}{2} + \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)}\right) + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}

producto

/       /pi\     /     /pi\     ___    /pi\                                         \     ___    /pi\                                         \ /       /pi\     /     /pi\     ___    /pi\                                         \     ___    /pi\                                         \ /                              _____________\
|    cos|--|     |  sin|--|   \/ 3 *cos|--|                                         |   \/ 3 *sin|--|                                         | |    cos|--|     |  sin|--|   \/ 3 *cos|--|                                         |   \/ 3 *sin|--|                                         | |                             /         ___ |
|       \9 /     |     \9 /            \9 /     /                1                 \|            \9 /     /                1                 \| |       \9 /     |     \9 /            \9 /     /                1                 \|            \9 /     /                1                 \| |            1               /  1   I*\/ 3  |
|1 - ------- + I*|- ------- - ------------- + im|----------------------------------|| + ------------- + re|----------------------------------||*|1 - ------- + I*|- ------- + ------------- + im|----------------------------------|| - ------------- + re|----------------------------------||*|1 + ------------------ + 3 /   - + ------- |
|       2        |     2            2           |     _____________                ||         2           |     _____________                || |       2        |     2            2           |     _____________                ||         2           |     _____________                || |         _____________   \/    2      2    |
|                |                              |    /         ___  /          ___\||                     |    /         ___  /          ___\|| |                |                              |    /         ___  /          ___\||                     |    /         ___  /          ___\|| |        /         ___                      |
|                |                              |   /  1   I*\/ 3   |  1   I*\/ 3 |||                     |   /  1   I*\/ 3   |  1   I*\/ 3 ||| |                |                              |   /  1   I*\/ 3   |  1   I*\/ 3 |||                     |   /  1   I*\/ 3   |  1   I*\/ 3 ||| |       /  1   I*\/ 3                       |
|                |                              |3 /   - + ------- *|- - - -------|||                     |3 /   - + ------- *|- - - -------||| |                |                              |3 /   - + ------- *|- - + -------|||                     |3 /   - + ------- *|- - + -------||| |    3 /   - + -------                      |
\                \                              \\/    2      2     \  2      2   ///                     \\/    2      2     \  2      2   /// \                \                              \\/    2      2     \  2      2   ///                     \\/    2      2     \  2      2   /// \    \/    2      2                         /

\left(- \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} + \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} + \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + 1 + i \left(- \frac{\sqrt{3} \cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sin{\left(\frac{\pi}{9} \right)}}{2} + \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)}\right)\right) \left(\operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} - \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + 1 + i \left(\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} - \frac{\sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} \cos{\left(\frac{\pi}{9} \right)}}{2}\right)\right) \left(1 + \frac{1}{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}} + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}\right)

                 /             _____________ /            _____________\\                               
/          /pi\\ |  3 ___   3 /         ___  |     2/3 3 /         ___ || /       ___    /pi\      /pi\\
|-2 + 4*sin|--||*\2*\/ 2  + \/  1 + I*\/ 3  *\2 + 2   *\/  1 + I*\/ 3  //*|-1 + \/ 3 *sin|--| + cos|--||
\          \18//                                                          \              \9 /      \9 //
--------------------------------------------------------------------------------------------------------
                                                _____________                                           
                                             3 /         ___                                            
                                           4*\/  1 + I*\/ 3

\frac{\left(-2 + 4 \sin{\left(\frac{\pi}{18} \right)}\right) \left(2 \sqrt[3]{2} + \sqrt[3]{1 + \sqrt{3} i} \left(2 + 2^{\frac{2}{3}} \sqrt[3]{1 + \sqrt{3} i}\right)\right) \left(-1 + \sqrt{3} \sin{\left(\frac{\pi}{9} \right)} + \cos{\left(\frac{\pi}{9} \right)}\right)}{4 \sqrt[3]{1 + \sqrt{3} i}}

(-2 + 4*sin(pi/18))*(2*2^(1/3) + (1 + i*sqrt(3))^(1/3)*(2 + 2^(2/3)*(1 + i*sqrt(3))^(1/3)))*(-1 + sqrt(3)*sin(pi/9) + cos(pi/9))/(4*(1 + i*sqrt(3))^(1/3))

Respuesta rápida [src]

            /pi\     /     /pi\     ___    /pi\                                         \     ___    /pi\                                         
         cos|--|     |  sin|--|   \/ 3 *cos|--|                                         |   \/ 3 *sin|--|                                         
            \9 /     |     \9 /            \9 /     /                1                 \|            \9 /     /                1                 \
x1 = 1 - ------- + I*|- ------- - ------------- + im|----------------------------------|| + ------------- + re|----------------------------------|
            2        |     2            2           |     _____________                ||         2           |     _____________                |
                     |                              |    /         ___  /          ___\||                     |    /         ___  /          ___\|
                     |                              |   /  1   I*\/ 3   |  1   I*\/ 3 |||                     |   /  1   I*\/ 3   |  1   I*\/ 3 ||
                     |                              |3 /   - + ------- *|- - - -------|||                     |3 /   - + ------- *|- - - -------||
                     \                              \\/    2      2     \  2      2   ///                     \\/    2      2     \  2      2   //

x_{1} = - \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} + \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} + \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + 1 + i \left(- \frac{\sqrt{3} \cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sin{\left(\frac{\pi}{9} \right)}}{2} + \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)}\right)

            /pi\     /     /pi\     ___    /pi\                                         \     ___    /pi\                                         
         cos|--|     |  sin|--|   \/ 3 *cos|--|                                         |   \/ 3 *sin|--|                                         
            \9 /     |     \9 /            \9 /     /                1                 \|            \9 /     /                1                 \
x2 = 1 - ------- + I*|- ------- + ------------- + im|----------------------------------|| - ------------- + re|----------------------------------|
            2        |     2            2           |     _____________                ||         2           |     _____________                |
                     |                              |    /         ___  /          ___\||                     |    /         ___  /          ___\|
                     |                              |   /  1   I*\/ 3   |  1   I*\/ 3 |||                     |   /  1   I*\/ 3   |  1   I*\/ 3 ||
                     |                              |3 /   - + ------- *|- - + -------|||                     |3 /   - + ------- *|- - + -------||
                     \                              \\/    2      2     \  2      2   ///                     \\/    2      2     \  2      2   //

x_{2} = \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} - \frac{\cos{\left(\frac{\pi}{9} \right)}}{2} - \frac{\sqrt{3} \sin{\left(\frac{\pi}{9} \right)}}{2} + 1 + i \left(\operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}}\right)} - \frac{\sin{\left(\frac{\pi}{9} \right)}}{2} + \frac{\sqrt{3} \cos{\left(\frac{\pi}{9} \right)}}{2}\right)

                                   _____________
                                  /         ___ 
                 1               /  1   I*\/ 3  
x3 = 1 + ------------------ + 3 /   - + ------- 
              _____________   \/    2      2    
             /         ___                      
            /  1   I*\/ 3                       
         3 /   - + -------                      
         \/    2      2

x_{3} = 1 + \frac{1}{\sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}} + \sqrt[3]{\frac{1}{2} + \frac{\sqrt{3} i}{2}}

x3 = 1 + (1/2 + sqrt(3)*i/2)^(-1/3) + (1/2 + sqrt(3)*i/2)^(1/3)

Respuesta numérica [src]

x1 = -0.532088886237956

x2 = 2.87938524157182

x3 = 0.652703644666139

x3 = 0.652703644666139

Gráfico

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Expresiones idénticas

Expresiones semejantes

x^3-3*x^2+1=0 la ecuación

Solución numérica:

Solución