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- La ecuación:
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Ecuación x^2-11*x+30=0
- Ecuación x^2+y^2=9
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Ecuación -33-y=-19
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Ecuación 11/(x-9)=-10
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -4*x+6*y=-7
- -7*x-13*y=5
- -18*x+8*y=-2
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Expresiones idénticas
- a*x+b*y+c= cero
- a multiplicar por x más b multiplicar por y más c es igual a 0
- a multiplicar por x más b multiplicar por y más c es igual a cero
- ax+by+c=0
- a*x+b*y+c=O
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Expresiones semejantes
- a*x+b*y-c=0
- a*x-b*y+c=0
- ax+by+c=0
a*x+b*y+c=0 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 (c + a*x + b*y)/x
Obtenemos la respuesta: x = -(c + b*y)/a
a*x+b*y+c = 0
Dividamos ambos miembros de la ecuación en (c + a*x + b*y)/x
x = 0 / ((c + a*x + b*y)/x)
Obtenemos la respuesta: x = -(c + b*y)/a
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x + b y + c = 0$$
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
$$a x + b y + c = 0$$
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
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)
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)