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Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación (x+9)^2=36*x
-
Ecuación a+120=2000/5
-
Ecuación -x/11+x=50/11
-
Ecuación x^2+7x+6=0
- Expresar {x} en función de y en la ecuación:
- 12*x+8*y=18
- 8*x+6*y=20
- -2*x+18*y=13
- -11*x-1*y=15
- Integral de d{x}:
- Ax+B
-
Expresiones idénticas
- Ax+B=c
- Ax más B es igual a c
-
Expresiones semejantes
- (A*x+B)*((x+1/2)^2+3/4)+(C*x+D)=1
- Ax-B=c
Ax+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 = (c - b)/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 = (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
$$a x + b = c$$
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)