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Otras calculadoras
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- La ecuación:
-
Ecuación x^4+2*x^2-8=0
-
Ecuación x*(x^2+8*x+16)=5*(x+4)
-
Ecuación -25-x=-17
-
Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
- Derivada de:
- ax+b
- Integral de d{x}:
- ax+b
-
Expresiones idénticas
- ax+b=cx+d
- ax más b es igual a cx más d
-
Expresiones semejantes
- a*x+b-b=0
- a*x+b=c
- a*x^3+b*x^2+c*x+d=0
- ax-b=cx+d
- ax+b=cx-d
- a*x+b*y+c=0
-
Expresiones con funciones
- ax
- ax^2+bx+c=0
- ax^2+8*x-4*a-16=0
- ax^2+ax+3=0
- ax^2+2x+3=0
- ax+8y=20
- 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=cx+d 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 = (d - b)/(a - c)
a*x+b = c*x+d
Dividamos ambos miembros de la ecuación en (b + a*x)/x
x = d + c*x / ((b + a*x)/x)
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)