Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x^2+5x=36
-
Ecuación 3*x=8
-
Ecuación 9-7(x+3)=5-6x
-
Ecuación 4x-5=3+2(x+1)
- Expresar {x} en función de y en la ecuación:
- -17*x+2*y=9
- 10*x-15*y=16
- -17*x+2*y=-4
- -2*x-19*y=3
- Derivada de:
- a*x
- Integral de d{x}:
- a*x
- Límite de la función:
- a*x
-
Expresiones idénticas
- a*x=-b*y-c
- a multiplicar por x es igual a menos b multiplicar por y menos c
- ax=-by-c
-
Expresiones semejantes
- a*x=+b*y-c
- abs(x^2-3*x-1)=(x^2-2*x-2)(a-3)/ax+2=5
- ax=-by-c÷ax
- a*x=-b*y+c
- (a(x-a))/(x-4)=0
a*x=-b*y-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 a
Obtenemos la respuesta: x = -(c + b*y)/a
a*x = -b*y-c
Dividamos ambos miembros de la ecuación en a
x = -c - b*y / (a)
Obtenemos la respuesta: x = -(c + b*y)/a
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x = - b y - c$$
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
$$b y + c - x = 0$$
su solución
$$x = b y + c$$
Con
$$a = 0$$
la ecuación será
$$b y + c = 0$$
su solución
$$a x = - b y - c$$
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
$$b y + c - x = 0$$
su solución
$$x = b y + c$$
Con
$$a = 0$$
la ecuación será
$$b y + c = 0$$
su solución
Gráfica
Respuesta rápida
[src]
/(re(c) + re(b*y))*im(a) (im(c) + im(b*y))*re(a)\ (im(c) + im(b*y))*im(a) (re(c) + re(b*y))*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)
$$x_{1} = i \left(\frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x1 = i*((re(c) + re(b*y))*im(a)/(re(a)^2 + im(a)^2) - (im(c) + im(b*y))*re(a)/(re(a)^2 + im(a)^2)) - (re(c) + re(b*y))*re(a)/(re(a)^2 + im(a)^2) - (im(c) + im(b*y))*im(a)/(re(a)^2 + im(a)^2)
Suma y producto de raíces
[src]
suma
/(re(c) + re(b*y))*im(a) (im(c) + im(b*y))*re(a)\ (im(c) + im(b*y))*im(a) (re(c) + re(b*y))*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)
$$i \left(\frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
/(re(c) + re(b*y))*im(a) (im(c) + im(b*y))*re(a)\ (im(c) + im(b*y))*im(a) (re(c) + re(b*y))*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)
$$i \left(\frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
producto
/(re(c) + re(b*y))*im(a) (im(c) + im(b*y))*re(a)\ (im(c) + im(b*y))*im(a) (re(c) + re(b*y))*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)
$$i \left(\frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
I*((re(c) + re(b*y))*im(a) - (im(c) + im(b*y))*re(a)) - (im(c) + im(b*y))*im(a) - (re(c) + re(b*y))*re(a)
---------------------------------------------------------------------------------------------------------
2 2
im (a) + re (a)
$$\frac{i \left(\left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)} - \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}\right) - \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(i*((re(c) + re(b*y))*im(a) - (im(c) + im(b*y))*re(a)) - (im(c) + im(b*y))*im(a) - (re(c) + re(b*y))*re(a))/(im(a)^2 + re(a)^2)