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- La ecuación:
-
Ecuación (x-3)*(x+2)=0
-
Ecuación (11x+14)-(5x-8)=25
-
Ecuación z^2-6*z+10=0
-
Ecuación 4/(x-4)=-5
- Expresar {x} en función de y en la ecuación:
- -7*x-13*y=5
- 15*x+1*y=19
- 7*x-1*y=-7
- -11*x-14*y=-3
-
Expresiones idénticas
- a*x-b=c
- a multiplicar por x menos b es igual a c
- ax-b=c
-
Expresiones semejantes
- a^x-b*x=0
- ax-b/a+b+bx+a/a-b=a^2+b^2/a^2-b^2
- a*x+b=c
a*x-b=c la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos una ecuación lineal:
Dividamos ambos miembros de la ecuación en (-b + a*x)/x
Obtenemos la respuesta: x = (b + c)/a
a*x-b = c
Dividamos ambos miembros de la ecuación en (-b + a*x)/x
x = c / ((-b + a*x)/x)
Obtenemos la respuesta: x = (b + c)/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
$$a x - b = c$$
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
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*((im(b) + im(c))*re(a) - (re(b) + re(c))*im(a)) + (im(b) + im(c))*im(a) + (re(b) + re(c))*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*((im(b) + im(c))*re(a) - (re(b) + re(c))*im(a)) + (im(b) + im(c))*im(a) + (re(b) + re(c))*re(a))/(im(a)^2 + re(a)^2)
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)