Sr Examen

ax+b-b=c-b la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

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

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
a*x = c-b

Sumamos los términos semejantes en el miembro derecho de la ecuación:
a*x = c - b

Dividamos ambos miembros de la ecuación en a
x = c - b / (a)

Obtenemos la respuesta: x = (c - b)/a
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x = - b + c$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$b - c - x = 0$$
su solución
$$x = b - c$$
Con
$$a = 0$$
la ecuación será
$$b - c = 0$$
su solución
Gráfica
Respuesta rápida [src]
       /(-im(b) + im(c))*re(a)   (-re(b) + re(c))*im(a)\   (-im(b) + im(c))*im(a)   (-re(b) + re(c))*re(a)
x1 = I*|---------------------- - ----------------------| + ---------------------- + ----------------------
       |     2        2               2        2       |        2        2               2        2       
       \   im (a) + re (a)          im (a) + re (a)    /      im (a) + re (a)          im (a) + re (a)    
$$x_{1} = i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x1 = i*(-(-re(b) + re(c))*im(a)/(re(a)^2 + im(a)^2) + (-im(b) + im(c))*re(a)/(re(a)^2 + im(a)^2)) + (-re(b) + re(c))*re(a)/(re(a)^2 + im(a)^2) + (-im(b) + im(c))*im(a)/(re(a)^2 + im(a)^2)
Suma y producto de raíces [src]
suma
  /(-im(b) + im(c))*re(a)   (-re(b) + re(c))*im(a)\   (-im(b) + im(c))*im(a)   (-re(b) + re(c))*re(a)
I*|---------------------- - ----------------------| + ---------------------- + ----------------------
  |     2        2               2        2       |        2        2               2        2       
  \   im (a) + re (a)          im (a) + re (a)    /      im (a) + re (a)          im (a) + re (a)    
$$i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
  /(-im(b) + im(c))*re(a)   (-re(b) + re(c))*im(a)\   (-im(b) + im(c))*im(a)   (-re(b) + re(c))*re(a)
I*|---------------------- - ----------------------| + ---------------------- + ----------------------
  |     2        2               2        2       |        2        2               2        2       
  \   im (a) + re (a)          im (a) + re (a)    /      im (a) + re (a)          im (a) + re (a)    
$$i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
producto
  /(-im(b) + im(c))*re(a)   (-re(b) + re(c))*im(a)\   (-im(b) + im(c))*im(a)   (-re(b) + re(c))*re(a)
I*|---------------------- - ----------------------| + ---------------------- + ----------------------
  |     2        2               2        2       |        2        2               2        2       
  \   im (a) + re (a)          im (a) + re (a)    /      im (a) + re (a)          im (a) + re (a)    
$$i \left(- \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
I*((-re(c) + re(b))*im(a) - (-im(c) + im(b))*re(a)) - (-im(c) + im(b))*im(a) - (-re(c) + re(b))*re(a)
-----------------------------------------------------------------------------------------------------
                                             2        2                                              
                                           im (a) + re (a)                                           
$$\frac{i \left(\left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(a\right)} - \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(a\right)}\right) - \left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(i*((-re(c) + re(b))*im(a) - (-im(c) + im(b))*re(a)) - (-im(c) + im(b))*im(a) - (-re(c) + re(b))*re(a))/(im(a)^2 + re(a)^2)