Sr Examen

Lang:

Otras calculadoras

¿Cómo usar?
La ecuación:
Ecuación 6*x^2+x-7=0
Ecuación z^5+32=0
Ecuación 2-5(3+2x)=17
Ecuación (6*x+8)/2+5=5*x/3
Expresar {x} en función de y en la ecuación:
-9*x-12*y=-19
-8*x+3*y=-4
16*x-17*y=-15
-10*x-12*y=-10
Expresiones idénticas
*x^ cuatro - treinta y dos *x- doce = cero
multiplicar por x en el grado 4 menos 32 multiplicar por x menos 12 es igual a 0
multiplicar por x en el grado cuatro menos treinta y dos multiplicar por x menos doce es igual a cero
*x4-32*x-12=0
*x⁴-32*x-12=0
x^4-32x-12=0
x4-32x-12=0
*x^4-32*x-12=O
Expresiones semejantes
*x^4+32*x-12=0
*x^4-32*x+12=0

x^4-32x-12=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

 4                
x  - 32*x - 12 = 0

$$\left(x^{4} - 32 x\right) - 12 = 0$$

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

                                                                  ____________________________________________________________________________________________________                                                                     ____________________________________________________________________________________________________                                                                         ____________________________________________________________________________________________________                                                                         ____________________________________________________________________________________________________
                                                                 /        _______________                                                                                                                                                 /        _______________                                                                                                                                                     /                             _______________                                                                                                                                /                             _______________                                                        
                                                                /      3 /          ____            8                                     64                                                                                             /      3 /          ____            8                                     64                                                                                                 /            8              3 /          ____                             64                                                                                                 /            8              3 /          ____                             64                          
                                                               /   - 2*\/  64 + 8*\/ 65   + ------------------ + ----------------------------------------------------                                                                   /   - 2*\/  64 + 8*\/ 65   + ------------------ + ----------------------------------------------------                                                             I*        /   - ------------------ + 2*\/  64 + 8*\/ 65   + ----------------------------------------------------                                                             I*        /   - ------------------ + 2*\/  64 + 8*\/ 65   + ---------------------------------------------------- 
       _____________________________________________          /                                _______________          _____________________________________________           _____________________________________________          /                                _______________          _____________________________________________             _____________________________________________            /         _______________                                 _____________________________________________             _____________________________________________            /         _______________                                 _____________________________________________ 
      /                             _______________          /                              3 /          ____          /                             _______________           /                             _______________          /                              3 /          ____          /                             _______________             /                             _______________            /       3 /          ____                                 /                             _______________             /                             _______________            /       3 /          ____                                 /                             _______________  
     /            8              3 /          ____          /                               \/  64 + 8*\/ 65          /            8              3 /          ____           /            8              3 /          ____          /                               \/  64 + 8*\/ 65          /            8              3 /          ____             /            8              3 /          ____            /        \/  64 + 8*\/ 65                                 /            8              3 /          ____             /            8              3 /          ____            /        \/  64 + 8*\/ 65                                 /            8              3 /          ____   
    /   - ------------------ + 2*\/  64 + 8*\/ 65          /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65           /   - ------------------ + 2*\/  64 + 8*\/ 65          /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65             /   - ------------------ + 2*\/  64 + 8*\/ 65            /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65             /   - ------------------ + 2*\/  64 + 8*\/ 65            /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65    
   /         _______________                              /                                                         /         _______________                               /         _______________                              /                                                         /         _______________                                 /         _______________                                /                                                         /         _______________                                 /         _______________                                /                                                         /         _______________                         
  /       3 /          ____                              /                                                         /       3 /          ____                               /       3 /          ____                              /                                                         /       3 /          ____                                 /       3 /          ____                                /                                                         /       3 /          ____                                 /       3 /          ____                                /                                                         /       3 /          ____                          
\/        \/  64 + 8*\/ 65                             \/                                                        \/        \/  64 + 8*\/ 65                              \/        \/  64 + 8*\/ 65                             \/                                                        \/        \/  64 + 8*\/ 65                                \/        \/  64 + 8*\/ 65                               \/                                                        \/        \/  64 + 8*\/ 65                                \/        \/  64 + 8*\/ 65                               \/                                                        \/        \/  64 + 8*\/ 65                           
---------------------------------------------------- + --------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------- - --------------------------------------------------------------------------------------------------------------- + - ---------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------- + - ---------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------
                         2                                                                                    2                                                                                   2                                                                                    2                                                                                     2                                                                                     2                                                                                      2                                                                                     2

$$\left(\left(\left(- \frac{\sqrt{- 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2} + \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2}\right) + \left(\frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2}\right)\right) + \left(- \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2} - \frac{i \sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2}\right)\right) + \left(- \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2} + \frac{i \sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2}\right)$$

$$0$$

producto

/                                                                  ____________________________________________________________________________________________________\ /                                                                  ____________________________________________________________________________________________________\ /                                                                      ____________________________________________________________________________________________________\ /                                                                      ____________________________________________________________________________________________________\
|                                                                 /        _______________                                                                             | |                                                                 /        _______________                                                                             | |                                                                     /                             _______________                                                        | |                                                                     /                             _______________                                                        |
|                                                                /      3 /          ____            8                                     64                          | |                                                                /      3 /          ____            8                                     64                          | |                                                                    /            8              3 /          ____                             64                          | |                                                                    /            8              3 /          ____                             64                          |
|                                                               /   - 2*\/  64 + 8*\/ 65   + ------------------ + ---------------------------------------------------- | |                                                               /   - 2*\/  64 + 8*\/ 65   + ------------------ + ---------------------------------------------------- | |                                                         I*        /   - ------------------ + 2*\/  64 + 8*\/ 65   + ---------------------------------------------------- | |                                                         I*        /   - ------------------ + 2*\/  64 + 8*\/ 65   + ---------------------------------------------------- |
|       _____________________________________________          /                                _______________          _____________________________________________ | |       _____________________________________________          /                                _______________          _____________________________________________ | |         _____________________________________________            /         _______________                                 _____________________________________________ | |         _____________________________________________            /         _______________                                 _____________________________________________ |
|      /                             _______________          /                              3 /          ____          /                             _______________  | |      /                             _______________          /                              3 /          ____          /                             _______________  | |        /                             _______________            /       3 /          ____                                 /                             _______________  | |        /                             _______________            /       3 /          ____                                 /                             _______________  |
|     /            8              3 /          ____          /                               \/  64 + 8*\/ 65          /            8              3 /          ____   | |     /            8              3 /          ____          /                               \/  64 + 8*\/ 65          /            8              3 /          ____   | |       /            8              3 /          ____            /        \/  64 + 8*\/ 65                                 /            8              3 /          ____   | |       /            8              3 /          ____            /        \/  64 + 8*\/ 65                                 /            8              3 /          ____   |
|    /   - ------------------ + 2*\/  64 + 8*\/ 65          /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65    | |    /   - ------------------ + 2*\/  64 + 8*\/ 65          /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65    | |      /   - ------------------ + 2*\/  64 + 8*\/ 65            /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65    | |      /   - ------------------ + 2*\/  64 + 8*\/ 65            /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65    |
|   /         _______________                              /                                                         /         _______________                         | |   /         _______________                              /                                                         /         _______________                         | |     /         _______________                                /                                                         /         _______________                         | |     /         _______________                                /                                                         /         _______________                         |
|  /       3 /          ____                              /                                                         /       3 /          ____                          | |  /       3 /          ____                              /                                                         /       3 /          ____                          | |    /       3 /          ____                                /                                                         /       3 /          ____                          | |    /       3 /          ____                                /                                                         /       3 /          ____                          |
|\/        \/  64 + 8*\/ 65                             \/                                                        \/        \/  64 + 8*\/ 65                           | |\/        \/  64 + 8*\/ 65                             \/                                                        \/        \/  64 + 8*\/ 65                           | |  \/        \/  64 + 8*\/ 65                               \/                                                        \/        \/  64 + 8*\/ 65                           | |  \/        \/  64 + 8*\/ 65                               \/                                                        \/        \/  64 + 8*\/ 65                           |
|---------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------|*|---------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------|*|- ---------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------|*|- ---------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------|
\                         2                                                                                    2                                                       / \                         2                                                                                    2                                                       / \                           2                                                                                     2                                                        / \                           2                                                                                     2                                                        /

$$\left(\frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2}\right) \left(- \frac{\sqrt{- 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2} + \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2}\right) \left(- \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2} - \frac{i \sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2}\right) \left(- \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2} + \frac{i \sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2}\right)$$

-12

$$-12$$

-12

Respuesta rápida [src]

                                                                       ____________________________________________________________________________________________________
                                                                      /        _______________                                                                             
                                                                     /      3 /          ____            8                                     64                          
                                                                    /   - 2*\/  64 + 8*\/ 65   + ------------------ + ---------------------------------------------------- 
            _____________________________________________          /                                _______________          _____________________________________________ 
           /                             _______________          /                              3 /          ____          /                             _______________  
          /            8              3 /          ____          /                               \/  64 + 8*\/ 65          /            8              3 /          ____   
         /   - ------------------ + 2*\/  64 + 8*\/ 65          /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65    
        /         _______________                              /                                                         /         _______________                         
       /       3 /          ____                              /                                                         /       3 /          ____                          
     \/        \/  64 + 8*\/ 65                             \/                                                        \/        \/  64 + 8*\/ 65                           
x1 = ---------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------
                              2                                                                                    2

$$x_{1} = \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2}$$

                                                                       ____________________________________________________________________________________________________
                                                                      /        _______________                                                                             
                                                                     /      3 /          ____            8                                     64                          
                                                                    /   - 2*\/  64 + 8*\/ 65   + ------------------ + ---------------------------------------------------- 
            _____________________________________________          /                                _______________          _____________________________________________ 
           /                             _______________          /                              3 /          ____          /                             _______________  
          /            8              3 /          ____          /                               \/  64 + 8*\/ 65          /            8              3 /          ____   
         /   - ------------------ + 2*\/  64 + 8*\/ 65          /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65    
        /         _______________                              /                                                         /         _______________                         
       /       3 /          ____                              /                                                         /       3 /          ____                          
     \/        \/  64 + 8*\/ 65                             \/                                                        \/        \/  64 + 8*\/ 65                           
x2 = ---------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------
                              2                                                                                    2

$$x_{2} = - \frac{\sqrt{- 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2} + \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2}$$

                                                                           ____________________________________________________________________________________________________
                                                                          /                             _______________                                                        
                                                                         /            8              3 /          ____                             64                          
                                                              I*        /   - ------------------ + 2*\/  64 + 8*\/ 65   + ---------------------------------------------------- 
              _____________________________________________            /         _______________                                 _____________________________________________ 
             /                             _______________            /       3 /          ____                                 /                             _______________  
            /            8              3 /          ____            /        \/  64 + 8*\/ 65                                 /            8              3 /          ____   
           /   - ------------------ + 2*\/  64 + 8*\/ 65            /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65    
          /         _______________                                /                                                         /         _______________                         
         /       3 /          ____                                /                                                         /       3 /          ____                          
       \/        \/  64 + 8*\/ 65                               \/                                                        \/        \/  64 + 8*\/ 65                           
x3 = - ---------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------
                                2                                                                                     2

$$x_{3} = - \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2} - \frac{i \sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2}$$

                                                                           ____________________________________________________________________________________________________
                                                                          /                             _______________                                                        
                                                                         /            8              3 /          ____                             64                          
                                                              I*        /   - ------------------ + 2*\/  64 + 8*\/ 65   + ---------------------------------------------------- 
              _____________________________________________            /         _______________                                 _____________________________________________ 
             /                             _______________            /       3 /          ____                                 /                             _______________  
            /            8              3 /          ____            /        \/  64 + 8*\/ 65                                 /            8              3 /          ____   
           /   - ------------------ + 2*\/  64 + 8*\/ 65            /                                                         /   - ------------------ + 2*\/  64 + 8*\/ 65    
          /         _______________                                /                                                         /         _______________                         
         /       3 /          ____                                /                                                         /       3 /          ____                          
       \/        \/  64 + 8*\/ 65                               \/                                                        \/        \/  64 + 8*\/ 65                           
x4 = - ---------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------
                                2                                                                                     2

$$x_{4} = - \frac{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}{2} + \frac{i \sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}} + \frac{64}{\sqrt{- \frac{8}{\sqrt[3]{64 + 8 \sqrt{65}}} + 2 \sqrt[3]{64 + 8 \sqrt{65}}}}}}{2}$$

x4 = -sqrt(-8/(64 + 8*sqrt(65))^(1/3) + 2*(64 + 8*sqrt(65))^(1/3))/2 + i*sqrt(-8/(64 + 8*sqrt(65))^(1/3) + 2*(64 + 8*sqrt(65))^(1/3) + 64/sqrt(-8/(64 + 8*sqrt(65))^(1/3) + 2*(64 + 8*sqrt(65))^(1/3)))/2

Respuesta numérica [src]

x1 = -0.374386056108728

x2 = -1.45834472324289 - 2.75906519915778*i

x3 = -1.45834472324289 + 2.75906519915778*i

x4 = 3.29107550259451

x4 = 3.29107550259451

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

*x^4-32*x-12=0 la ecuación

Solución numérica:

Solución

x^4-32x-12=0 la ecuación