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
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]
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)
$$i \left(\frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(\operatorname{re}{\left(x\right)} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} - 1\right) \left(\operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
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)