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La ecuación:
Ecuación x^2+5x=36
Ecuación 3*x=8
Ecuación 9-7(x+3)=5-6x
Ecuación 4x-5=3+2(x+1)
Expresar {x} en función de y en la ecuación:
-17*x+2*y=9
10*x-15*y=16
-17*x+2*y=-4
-2*x-19*y=3
Gráfico de la función y =:
x.diff(x)
Expresiones idénticas
x.diff(x)=(uno +y^ dos)/(tres *x^ dos)
x.diff(x) es igual a (1 más y al cuadrado ) dividir por (3 multiplicar por x al cuadrado )
x.diff(x) es igual a (uno más y en el grado dos) dividir por (tres multiplicar por x en el grado dos)
x.diff(x)=(1+y2)/(3*x2)
x.diffx=1+y2/3*x2
x.diff(x)=(1+y²)/(3*x²)
x.diff(x)=(1+y en el grado 2)/(3*x en el grado 2)
x.diff(x)=(1+y^2)/(3x^2)
x.diff(x)=(1+y2)/(3x2)
x.diffx=1+y2/3x2
x.diffx=1+y^2/3x^2
x.diff(x)=(1+y^2) dividir por (3*x^2)
Expresiones semejantes
x.diff(x)=(1-y^2)/(3*x^2)

x.diff(x)=(1+y^2)/(3*x^2) la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

/x  for 0 = 1        2
|               1 + y 
<1  for 1 = 1 = ------
|                   2 
\0  otherwise    3*x

$$\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = \frac{y^{2} + 1}{3 x^{2}}$$

Simplificar

Solución detallada

Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.

La ecuación se convierte de
$$\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = \frac{y^{2} + 1}{3 x^{2}}$$
en
$$\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} - \frac{y^{2} + 1}{3 x^{2}} = 0$$
Abramos la expresión en la ecuación
$$\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} - \frac{y^{2} + 1}{3 x^{2}} = 0$$
Obtenemos la ecuación cuadrática
$$\begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} - \frac{y^{2}}{3 x^{2}} - \frac{1}{3 x^{2}} = 0$$
Es la ecuación de la forma

a*y^2 + b*y + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = - \frac{1}{3 x^{2}}$$
$$b = 0$$
$$c = 1 - \frac{1}{3 x^{2}}$$
, entonces

D = b^2 - 4 * a * c =

(0)^2 - 4 * (-1/(3*x^2)) * (1 - 1/(3*x^2)) = 4*(1 - 1/(3*x^2))/(3*x^2)

La ecuación tiene dos raíces.

y1 = (-b + sqrt(D)) / (2*a)

y2 = (-b - sqrt(D)) / (2*a)

o
$$y_{1} = - \sqrt{3} x^{2} \sqrt{\frac{1 - \frac{1}{3 x^{2}}}{x^{2}}}$$
$$y_{2} = \sqrt{3} x^{2} \sqrt{\frac{1 - \frac{1}{3 x^{2}}}{x^{2}}}$$

Gráfica

Respuesta rápida [src]

           ________________________________________________                                                             ________________________________________________                                                    
          /                           2                        /     /                        2          2   \\        /                           2                        /     /                        2          2   \\
       4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|     4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|
y1 = - \/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *cos|----------------------------------------------| - I*\/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *sin|----------------------------------------------|
                                                               \                      2                       /                                                             \                      2                       /

$$y_{1} = - i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)} - \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)}$$

         ________________________________________________                                                             ________________________________________________                                                    
        /                           2                        /     /                        2          2   \\        /                           2                        /     /                        2          2   \\
     4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|     4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|
y2 = \/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *cos|----------------------------------------------| + I*\/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *sin|----------------------------------------------|
                                                             \                      2                       /                                                             \                      2                       /

$$y_{2} = i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)} + \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)}$$

y2 = i*((3*re(x)^2 - 3*im(x)^2 - 1)^2 + 36*re(x)^2*im(x)^2)^(1/4)*sin(atan2(6*re(x)*im(x, 3*re(x)^2 - 3*im(x)^2 - 1)/2) + ((3*re(x)^2 - 3*im(x)^2 - 1)^2 + 36*re(x)^2*im(x)^2)^(1/4)*cos(atan2(6*re(x)*im(x), 3*re(x)^2 - 3*im(x)^2 - 1)/2))

Suma y producto de raíces [src]

suma

      ________________________________________________                                                             ________________________________________________                                                           ________________________________________________                                                             ________________________________________________                                                    
     /                           2                        /     /                        2          2   \\        /                           2                        /     /                        2          2   \\      /                           2                        /     /                        2          2   \\        /                           2                        /     /                        2          2   \\
  4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|     4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|   4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|     4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|
- \/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *cos|----------------------------------------------| - I*\/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *sin|----------------------------------------------| + \/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *cos|----------------------------------------------| + I*\/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *sin|----------------------------------------------|
                                                          \                      2                       /                                                             \                      2                       /                                                           \                      2                       /                                                             \                      2                       /

$$\left(- i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)} - \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)} + \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)}\right)$$

$$0$$

producto

/      ________________________________________________                                                             ________________________________________________                                                    \ /    ________________________________________________                                                             ________________________________________________                                                    \
|     /                           2                        /     /                        2          2   \\        /                           2                        /     /                        2          2   \\| |   /                           2                        /     /                        2          2   \\        /                           2                        /     /                        2          2   \\|
|  4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|     4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|| |4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/|     4 /  /         2          2   \         2      2        |atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/||
|- \/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *cos|----------------------------------------------| - I*\/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *sin|----------------------------------------------||*|\/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *cos|----------------------------------------------| + I*\/   \-1 - 3*im (x) + 3*re (x)/  + 36*im (x)*re (x) *sin|----------------------------------------------||
\                                                          \                      2                       /                                                             \                      2                       // \                                                        \                      2                       /                                                             \                      2                       //

$$\left(- i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)} - \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)} + \sqrt[4]{\left(3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}{2} \right)}\right)$$

     _______________________________________________                                                  
    /                          2                             /                        2          2   \
   /  /        2          2   \         2      2      I*atan2\6*im(x)*re(x), -1 - 3*im (x) + 3*re (x)/
-\/   \1 - 3*re (x) + 3*im (x)/  + 36*im (x)*re (x) *e

$$- \sqrt{\left(- 3 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right)^{2} + 36 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(6 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},3 \left(\operatorname{re}{\left(x\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(x\right)}\right)^{2} - 1 \right)}}$$

-sqrt((1 - 3*re(x)^2 + 3*im(x)^2)^2 + 36*im(x)^2*re(x)^2)*exp(i*atan2(6*im(x)*re(x), -1 - 3*im(x)^2 + 3*re(x)^2))

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones semejantes

x.diff(x)=(1+y^2)/(3*x^2) la ecuación

Solución numérica:

Solución