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ax=a+1+x la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
a*x = a + 1 + x
$$a x = x + \left(a + 1\right)$$
Solución detallada
Tenemos una ecuación lineal:
a*x = a+1+x

Sumamos los términos semejantes en el miembro derecho de la ecuación:
a*x = 1 + a + x

Transportamos los términos con la incógnita a
del miembro derecho al izquierdo:
$$a x - a = x + 1$$
Dividamos ambos miembros de la ecuación en (-a + a*x)/a
a = 1 + x / ((-a + a*x)/a)

Obtenemos la respuesta: a = (1 + x)/(-1 + x)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x = a + x + 1$$
Коэффициент при a равен
$$x - 1$$
entonces son posibles los casos para x :
$$x < 1$$
$$x = 1$$
Consideremos todos los casos con detalles:
Con
$$x < 1$$
la ecuación será
$$- a - 1 = 0$$
su solución
$$a = -1$$
Con
$$x = 1$$
la ecuación será
$$-2 = 0$$
su solución
no hay soluciones
Gráfica
Respuesta rápida [src]
                                                                     2                                      
       /  (-1 + re(x))*im(x)       (1 + re(x))*im(x)   \           im (x)           (1 + re(x))*(-1 + re(x))
a1 = I*|---------------------- - ----------------------| + ---------------------- + ------------------------
       |            2     2                  2     2   |               2     2                   2     2    
       \(-1 + re(x))  + im (x)   (-1 + re(x))  + im (x)/   (-1 + re(x))  + im (x)    (-1 + re(x))  + im (x) 
$$a_{1} = i \left(\frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(\operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
a1 = i*((re(x) - 1)*im(x)/((re(x) - 1)^2 + im(x)^2) - (re(x) + 1)*im(x)/((re(x) - 1)^2 + im(x)^2)) + (re(x) - 1)*(re(x) + 1)/((re(x) - 1)^2 + im(x)^2) + im(x)^2/((re(x) - 1)^2 + im(x)^2)
Suma y producto de raíces [src]
suma
                                                                2                                      
  /  (-1 + re(x))*im(x)       (1 + re(x))*im(x)   \           im (x)           (1 + re(x))*(-1 + re(x))
I*|---------------------- - ----------------------| + ---------------------- + ------------------------
  |            2     2                  2     2   |               2     2                   2     2    
  \(-1 + re(x))  + im (x)   (-1 + re(x))  + im (x)/   (-1 + re(x))  + im (x)    (-1 + re(x))  + im (x) 
$$i \left(\frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(\operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
=
                                                                2                                      
  /  (-1 + re(x))*im(x)       (1 + re(x))*im(x)   \           im (x)           (1 + re(x))*(-1 + re(x))
I*|---------------------- - ----------------------| + ---------------------- + ------------------------
  |            2     2                  2     2   |               2     2                   2     2    
  \(-1 + re(x))  + im (x)   (-1 + re(x))  + im (x)/   (-1 + re(x))  + im (x)    (-1 + re(x))  + im (x) 
$$i \left(\frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(\operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
producto
                                                                2                                      
  /  (-1 + re(x))*im(x)       (1 + re(x))*im(x)   \           im (x)           (1 + re(x))*(-1 + re(x))
I*|---------------------- - ----------------------| + ---------------------- + ------------------------
  |            2     2                  2     2   |               2     2                   2     2    
  \(-1 + re(x))  + im (x)   (-1 + re(x))  + im (x)/   (-1 + re(x))  + im (x)    (-1 + re(x))  + im (x) 
$$i \left(\frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(\operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
=
  2                                          
im (x) + (1 + re(x))*(-1 + re(x)) - 2*I*im(x)
---------------------------------------------
                        2     2              
            (-1 + re(x))  + im (x)           
$$\frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(\operatorname{re}{\left(x\right)} + 1\right) + \left(\operatorname{im}{\left(x\right)}\right)^{2} - 2 i \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
(im(x)^2 + (1 + re(x))*(-1 + re(x)) - 2*i*im(x))/((-1 + re(x))^2 + im(x)^2)