Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación x^2-6x+9=0
-
Ecuación (x-11)^4=(x+3)^4
-
Ecuación √(x^2-1)^3=2*x
-
Ecuación -x/12+x=55/12
- Expresar {x} en función de y en la ecuación:
- 18*x-11*y=2
- 12*x-14*y=20
- -3*x-20*y=-13
- -16*x+14*y=-9
-
Expresiones idénticas
- ax+b-b=cx+d-b
- ax más b menos b es igual a cx más d menos b
-
Expresiones semejantes
- ax-b-b=cx+d-b
- ax+b-b=cx+d+b
- ax+b-b=cx-d-b
- ax+b+b=cx+d-b
- a*x+b-b=0
-
Expresiones con funciones
- ax
- ax=2x+1
- ax=-2
- ax^2+bx+c=0
- ax+b=cx+d
- ax^2+8*x-4*a-16=0
- cx
- cx^2-6cx+3x=15-5c
- Cx-1^x*(x-1)=30
- Cx-1x=10
- Cx+1^2+Cx+1^3=7x
- cx^((x^-2))=28
ax+b-b=cx+d-b la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
a*x + b - b = c*x + d - b
$$- b + \left(a x + b\right) = - b + \left(c x + d\right)$$
Solución detallada
Tenemos una ecuación lineal:
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
Sumamos los términos semejantes en el miembro derecho de la ecuación:
Dividamos ambos miembros de la ecuación en a
Obtenemos la respuesta: x = (d - b)/(a - c)
a*x+b-b = c*x+d-b
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
a*x = c*x+d-b
Sumamos los términos semejantes en el miembro derecho de la ecuación:
a*x = d - b + c*x
Dividamos ambos miembros de la ecuación en a
x = d - b + c*x / (a)
Obtenemos la respuesta: x = (d - b)/(a - c)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x = - b + c x + d$$
Коэффициент при x равен
$$a - c$$
entonces son posibles los casos para a :
$$a < c$$
$$a = c$$
Consideremos todos los casos con detalles:
Con
$$a < c$$
la ecuación será
$$b - c x - d + x \left(c - 1\right) = 0$$
su solución
$$x = b - d$$
Con
$$a = c$$
la ecuación será
$$b - d = 0$$
su solución
$$a x = - b + c x + d$$
Коэффициент при x равен
$$a - c$$
entonces son posibles los casos para a :
$$a < c$$
$$a = c$$
Consideremos todos los casos con detalles:
Con
$$a < c$$
la ecuación será
$$b - c x - d + x \left(c - 1\right) = 0$$
su solución
$$x = b - d$$
Con
$$a = c$$
la ecuación será
$$b - d = 0$$
su solución
Gráfica
Respuesta rápida
[src]
/ (-im(a) + im(c))*(-re(b) + re(d)) (-im(b) + im(d))*(-re(c) + re(a)) \ (-re(b) + re(d))*(-re(c) + re(a)) (-im(a) + im(c))*(-im(b) + im(d))
x1 = I*|------------------------------------- + -------------------------------------| + ------------------------------------- - -------------------------------------
| 2 2 2 2| 2 2 2 2
\(-im(c) + im(a)) + (-re(c) + re(a)) (-im(c) + im(a)) + (-re(c) + re(a)) / (-im(c) + im(a)) + (-re(c) + re(a)) (-im(c) + im(a)) + (-re(c) + re(a))
$$x_{1} = i \left(\frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right) \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}$$
x1 = i*((re(a) - re(c))*(-im(b) + im(d))/((re(a) - re(c))^2 + (im(a) - im(c))^2) + (-re(b) + re(d))*(-im(a) + im(c))/((re(a) - re(c))^2 + (im(a) - im(c))^2)) + (re(a) - re(c))*(-re(b) + re(d))/((re(a) - re(c))^2 + (im(a) - im(c))^2) - (-im(a) + im(c))*(-im(b) + im(d))/((re(a) - re(c))^2 + (im(a) - im(c))^2)
Suma y producto de raíces
[src]
suma
/ (-im(a) + im(c))*(-re(b) + re(d)) (-im(b) + im(d))*(-re(c) + re(a)) \ (-re(b) + re(d))*(-re(c) + re(a)) (-im(a) + im(c))*(-im(b) + im(d)) I*|------------------------------------- + -------------------------------------| + ------------------------------------- - ------------------------------------- | 2 2 2 2| 2 2 2 2 \(-im(c) + im(a)) + (-re(c) + re(a)) (-im(c) + im(a)) + (-re(c) + re(a)) / (-im(c) + im(a)) + (-re(c) + re(a)) (-im(c) + im(a)) + (-re(c) + re(a))
$$i \left(\frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right) \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}$$
=
/ (-im(a) + im(c))*(-re(b) + re(d)) (-im(b) + im(d))*(-re(c) + re(a)) \ (-re(b) + re(d))*(-re(c) + re(a)) (-im(a) + im(c))*(-im(b) + im(d)) I*|------------------------------------- + -------------------------------------| + ------------------------------------- - ------------------------------------- | 2 2 2 2| 2 2 2 2 \(-im(c) + im(a)) + (-re(c) + re(a)) (-im(c) + im(a)) + (-re(c) + re(a)) / (-im(c) + im(a)) + (-re(c) + re(a)) (-im(c) + im(a)) + (-re(c) + re(a))
$$i \left(\frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right) \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}$$
producto
/ (-im(a) + im(c))*(-re(b) + re(d)) (-im(b) + im(d))*(-re(c) + re(a)) \ (-re(b) + re(d))*(-re(c) + re(a)) (-im(a) + im(c))*(-im(b) + im(d)) I*|------------------------------------- + -------------------------------------| + ------------------------------------- - ------------------------------------- | 2 2 2 2| 2 2 2 2 \(-im(c) + im(a)) + (-re(c) + re(a)) (-im(c) + im(a)) + (-re(c) + re(a)) / (-im(c) + im(a)) + (-re(c) + re(a)) (-im(c) + im(a)) + (-re(c) + re(a))
$$i \left(\frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right) \left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}} - \frac{\left(- \operatorname{im}{\left(a\right)} + \operatorname{im}{\left(c\right)}\right) \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}$$
=
I*((-im(c) + im(a))*(-re(d) + re(b)) - (-im(d) + im(b))*(-re(c) + re(a))) - (-im(c) + im(a))*(-im(d) + im(b)) - (-re(c) + re(a))*(-re(d) + re(b))
-------------------------------------------------------------------------------------------------------------------------------------------------
2 2
(-im(c) + im(a)) + (-re(c) + re(a))
$$\frac{i \left(- \left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(d\right)}\right) + \left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(d\right)}\right) \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)\right) - \left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right) \left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(d\right)}\right) - \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right) \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(d\right)}\right)}{\left(\operatorname{re}{\left(a\right)} - \operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)} - \operatorname{im}{\left(c\right)}\right)^{2}}$$
(i*((-im(c) + im(a))*(-re(d) + re(b)) - (-im(d) + im(b))*(-re(c) + re(a))) - (-im(c) + im(a))*(-im(d) + im(b)) - (-re(c) + re(a))*(-re(d) + re(b)))/((-im(c) + im(a))^2 + (-re(c) + re(a))^2)