Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 3x^2+13x-10=0
-
Ecuación -3(1-3x)-12=12
-
Ecuación 2*x^2-x-10=0
-
Ecuación 2^x=17
- Expresar {x} en función de y en la ecuación:
- -18*x-8*y=-18
- -13*x+12*y=-19
- -1*x+11*y=-9
- 16*x-11*y=13
-
Expresiones idénticas
- (a+x)*(b+y)+c= cero
- (a más x) multiplicar por (b más y) más c es igual a 0
- (a más x) multiplicar por (b más y) más c es igual a cero
- (a+x)(b+y)+c=0
- a+xb+y+c=0
- (a+x)*(b+y)+c=O
-
Expresiones semejantes
- (a-x)*(b+y)+c=0
- (a+x)*(b+y)-c=0
- (a+x)*(b-y)+c=0
(a+x)*(b+y)+c=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación:
Abrimos la expresión:
Reducimos, obtenemos:
Dividamos ambos miembros de la ecuación en (c + a*b + a*y + b*x + x*y)/x
Obtenemos la respuesta: x = -(c + a*b + a*y)/(b + y)
(a+x)*(b+y)+c = 0
Abrimos la expresión:
a*b + a*y + b*x + x*y + c = 0
Reducimos, obtenemos:
c + a*b + a*y + b*x + x*y = 0
Dividamos ambos miembros de la ecuación en (c + a*b + a*y + b*x + x*y)/x
x = 0 / ((c + a*b + a*y + b*x + x*y)/x)
Obtenemos la respuesta: x = -(c + a*b + a*y)/(b + y)
Gráfica
Respuesta rápida
[src]
/ (-im(b) - im(y))*(re(c) + re(a*b) + re(a*y)) (re(b) + re(y))*(im(c) + im(a*b) + im(a*y))\ (-im(b) - im(y))*(im(c) + im(a*b) + im(a*y)) (re(b) + re(y))*(re(c) + re(a*b) + re(a*y))
x1 = I*|- -------------------------------------------- - -------------------------------------------| + -------------------------------------------- - -------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ (im(b) + im(y)) + (re(b) + re(y)) (im(b) + im(y)) + (re(b) + re(y)) / (im(b) + im(y)) + (re(b) + re(y)) (im(b) + im(y)) + (re(b) + re(y))
$$x_{1} = i \left(- \frac{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(b\right)} - \operatorname{im}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} - \operatorname{im}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}}$$
x1 = i*(-(re(b) + re(y))*(im(c) + im(a*b) + im(a*y))/((re(b) + re(y))^2 + (im(b) + im(y))^2) - (-im(b) - im(y))*(re(c) + re(a*b) + re(a*y))/((re(b) + re(y))^2 + (im(b) + im(y))^2)) - (re(b) + re(y))*(re(c) + re(a*b) + re(a*y))/((re(b) + re(y))^2 + (im(b) + im(y))^2) + (-im(b) - im(y))*(im(c) + im(a*b) + im(a*y))/((re(b) + re(y))^2 + (im(b) + im(y))^2)
Suma y producto de raíces
[src]
suma
/ (-im(b) - im(y))*(re(c) + re(a*b) + re(a*y)) (re(b) + re(y))*(im(c) + im(a*b) + im(a*y))\ (-im(b) - im(y))*(im(c) + im(a*b) + im(a*y)) (re(b) + re(y))*(re(c) + re(a*b) + re(a*y)) I*|- -------------------------------------------- - -------------------------------------------| + -------------------------------------------- - ------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ (im(b) + im(y)) + (re(b) + re(y)) (im(b) + im(y)) + (re(b) + re(y)) / (im(b) + im(y)) + (re(b) + re(y)) (im(b) + im(y)) + (re(b) + re(y))
$$i \left(- \frac{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(b\right)} - \operatorname{im}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} - \operatorname{im}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}}$$
=
/ (-im(b) - im(y))*(re(c) + re(a*b) + re(a*y)) (re(b) + re(y))*(im(c) + im(a*b) + im(a*y))\ (-im(b) - im(y))*(im(c) + im(a*b) + im(a*y)) (re(b) + re(y))*(re(c) + re(a*b) + re(a*y)) I*|- -------------------------------------------- - -------------------------------------------| + -------------------------------------------- - ------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ (im(b) + im(y)) + (re(b) + re(y)) (im(b) + im(y)) + (re(b) + re(y)) / (im(b) + im(y)) + (re(b) + re(y)) (im(b) + im(y)) + (re(b) + re(y))
$$i \left(- \frac{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(b\right)} - \operatorname{im}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} - \operatorname{im}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}}$$
producto
/ (-im(b) - im(y))*(re(c) + re(a*b) + re(a*y)) (re(b) + re(y))*(im(c) + im(a*b) + im(a*y))\ (-im(b) - im(y))*(im(c) + im(a*b) + im(a*y)) (re(b) + re(y))*(re(c) + re(a*b) + re(a*y)) I*|- -------------------------------------------- - -------------------------------------------| + -------------------------------------------- - ------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ (im(b) + im(y)) + (re(b) + re(y)) (im(b) + im(y)) + (re(b) + re(y)) / (im(b) + im(y)) + (re(b) + re(y)) (im(b) + im(y)) + (re(b) + re(y))
$$i \left(- \frac{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(b\right)} - \operatorname{im}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}}\right) - \frac{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b\right)} - \operatorname{im}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}}$$
=
I*((im(b) + im(y))*(re(c) + re(a*b) + re(a*y)) - (re(b) + re(y))*(im(c) + im(a*b) + im(a*y))) - (im(b) + im(y))*(im(c) + im(a*b) + im(a*y)) - (re(b) + re(y))*(re(c) + re(a*b) + re(a*y))
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
(im(b) + im(y)) + (re(b) + re(y))
$$\frac{i \left(- \left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right) + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right)\right) - \left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right) \left(\operatorname{re}{\left(c\right)} + \operatorname{re}{\left(a b\right)} + \operatorname{re}{\left(a y\right)}\right) - \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right) \left(\operatorname{im}{\left(c\right)} + \operatorname{im}{\left(a b\right)} + \operatorname{im}{\left(a y\right)}\right)}{\left(\operatorname{re}{\left(b\right)} + \operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(b\right)} + \operatorname{im}{\left(y\right)}\right)^{2}}$$
(i*((im(b) + im(y))*(re(c) + re(a*b) + re(a*y)) - (re(b) + re(y))*(im(c) + im(a*b) + im(a*y))) - (im(b) + im(y))*(im(c) + im(a*b) + im(a*y)) - (re(b) + re(y))*(re(c) + re(a*b) + re(a*y)))/((im(b) + im(y))^2 + (re(b) + re(y))^2)