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- La ecuación:
-
Ecuación 3^x+4^x=5^x
-
Ecuación (x-2)^4+3*(x-2)^2-10=0
-
Ecuación x+2/x=3
-
Ecuación x^2=-2
- Expresar {x} en función de y en la ecuación:
- 15*x+10*y=-4
- -9*x-15*y=-4
- -13*x+7*y=11
- -7*x-7*y=-14
-
Expresiones idénticas
- xy+5y= uno 2x^ cuatro +x+1
- xy más 5y es igual a 12x en el grado 4 más x más 1
- xy más 5y es igual a uno 2x en el grado cuatro más x más 1
- xy+5y=12x4+x+1
- xy+5y=12x⁴+x+1
-
Expresiones semejantes
- xy-5y=12x^4+x+1
- 2*x^2-16*x-x*y+5*y=-34
- 2*x^2-3*x*y+5*y=0
- 13*x^2-6*x*y+5*y^2=0
- xy+5y=12x^4+x-1
- xy+5y=12x^4-x+1
-
Expresiones con funciones
- xy
- xy²=539(y+1)
- xy-y^2=5x^2
- xy=-14
- xy=y^2+1
- xy+lny-2cosx=0
xy+5y=12x^4+x+1 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 (5*y + x*y)/y
Obtenemos la respuesta: y = (1 + x + 12*x^4)/(5 + x)
x*y+5*y = 12*x^4+x+1
Dividamos ambos miembros de la ecuación en (5*y + x*y)/y
y = 1 + x + 12*x^4 / ((5*y + x*y)/y)
Obtenemos la respuesta: y = (1 + x + 12*x^4)/(5 + x)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$x y + 5 y = 12 x^{4} + x + 1$$
Коэффициент при y равен
$$x + 5$$
entonces son posibles los casos para x :
$$x < -5$$
$$x = -5$$
Consideremos todos los casos con detalles:
Con
$$x < -5$$
la ecuación será
$$- y - 15547 = 0$$
su solución
$$y = -15547$$
Con
$$x = -5$$
la ecuación será
$$-7496 = 0$$
su solución
no hay soluciones
$$x y + 5 y = 12 x^{4} + x + 1$$
Коэффициент при y равен
$$x + 5$$
entonces son posibles los casos para x :
$$x < -5$$
$$x = -5$$
Consideremos todos los casos con detalles:
Con
$$x < -5$$
la ecuación será
$$- y - 15547 = 0$$
su solución
$$y = -15547$$
Con
$$x = -5$$
la ecuación será
$$-7496 = 0$$
su solución
no hay soluciones
Gráfica
Respuesta rápida
[src]
/ / 3 3 \ / 4 4 2 2 \ \ / 4 4 2 2 \ / 3 3 \
|(5 + re(x))*\- 48*im (x)*re(x) + 48*re (x)*im(x) + im(x)/ \1 + 12*im (x) + 12*re (x) - 72*im (x)*re (x) + re(x)/*im(x)| (5 + re(x))*\1 + 12*im (x) + 12*re (x) - 72*im (x)*re (x) + re(x)/ \- 48*im (x)*re(x) + 48*re (x)*im(x) + im(x)/*im(x)
y1 = I*|--------------------------------------------------------- - ------------------------------------------------------------| + ------------------------------------------------------------------ + ---------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ (5 + re(x)) + im (x) (5 + re(x)) + im (x) / (5 + re(x)) + im (x) (5 + re(x)) + im (x)
$$y_{1} = i \left(\frac{\left(\operatorname{re}{\left(x\right)} + 5\right) \left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \operatorname{im}{\left(x\right)}\right)}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(12 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} + 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} + 5\right) \left(12 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} + 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 1\right)}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
y1 = i*((re(x) + 5)*(48*re(x)^3*im(x) - 48*re(x)*im(x)^3 + im(x))/((re(x) + 5)^2 + im(x)^2) - (12*re(x)^4 - 72*re(x)^2*im(x)^2 + re(x) + 12*im(x)^4 + 1)*im(x)/((re(x) + 5)^2 + im(x)^2)) + (re(x) + 5)*(12*re(x)^4 - 72*re(x)^2*im(x)^2 + re(x) + 12*im(x)^4 + 1)/((re(x) + 5)^2 + im(x)^2) + (48*re(x)^3*im(x) - 48*re(x)*im(x)^3 + im(x))*im(x)/((re(x) + 5)^2 + im(x)^2)
Suma y producto de raíces
[src]
suma
/ / 3 3 \ / 4 4 2 2 \ \ / 4 4 2 2 \ / 3 3 \ |(5 + re(x))*\- 48*im (x)*re(x) + 48*re (x)*im(x) + im(x)/ \1 + 12*im (x) + 12*re (x) - 72*im (x)*re (x) + re(x)/*im(x)| (5 + re(x))*\1 + 12*im (x) + 12*re (x) - 72*im (x)*re (x) + re(x)/ \- 48*im (x)*re(x) + 48*re (x)*im(x) + im(x)/*im(x) I*|--------------------------------------------------------- - ------------------------------------------------------------| + ------------------------------------------------------------------ + --------------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ (5 + re(x)) + im (x) (5 + re(x)) + im (x) / (5 + re(x)) + im (x) (5 + re(x)) + im (x)
$$i \left(\frac{\left(\operatorname{re}{\left(x\right)} + 5\right) \left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \operatorname{im}{\left(x\right)}\right)}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(12 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} + 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} + 5\right) \left(12 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} + 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 1\right)}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
=
/ / 3 3 \ / 4 4 2 2 \ \ / 4 4 2 2 \ / 3 3 \ |(5 + re(x))*\- 48*im (x)*re(x) + 48*re (x)*im(x) + im(x)/ \1 + 12*im (x) + 12*re (x) - 72*im (x)*re (x) + re(x)/*im(x)| (5 + re(x))*\1 + 12*im (x) + 12*re (x) - 72*im (x)*re (x) + re(x)/ \- 48*im (x)*re(x) + 48*re (x)*im(x) + im(x)/*im(x) I*|--------------------------------------------------------- - ------------------------------------------------------------| + ------------------------------------------------------------------ + --------------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ (5 + re(x)) + im (x) (5 + re(x)) + im (x) / (5 + re(x)) + im (x) (5 + re(x)) + im (x)
$$i \left(\frac{\left(\operatorname{re}{\left(x\right)} + 5\right) \left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \operatorname{im}{\left(x\right)}\right)}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(12 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} + 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} + 5\right) \left(12 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} + 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 1\right)}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
producto
/ / 3 3 \ / 4 4 2 2 \ \ / 4 4 2 2 \ / 3 3 \ |(5 + re(x))*\- 48*im (x)*re(x) + 48*re (x)*im(x) + im(x)/ \1 + 12*im (x) + 12*re (x) - 72*im (x)*re (x) + re(x)/*im(x)| (5 + re(x))*\1 + 12*im (x) + 12*re (x) - 72*im (x)*re (x) + re(x)/ \- 48*im (x)*re(x) + 48*re (x)*im(x) + im(x)/*im(x) I*|--------------------------------------------------------- - ------------------------------------------------------------| + ------------------------------------------------------------------ + --------------------------------------------------- | 2 2 2 2 | 2 2 2 2 \ (5 + re(x)) + im (x) (5 + re(x)) + im (x) / (5 + re(x)) + im (x) (5 + re(x)) + im (x)
$$i \left(\frac{\left(\operatorname{re}{\left(x\right)} + 5\right) \left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \operatorname{im}{\left(x\right)}\right)}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{\left(12 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} + 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(x\right)} + 5\right) \left(12 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} + 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 1\right)}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} + \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
=
2 / 3 2 \ / 4 4 2 2 \ / 4 4 / 3 2 \ 2 2 \
im (x)*\1 + 48*re (x) - 48*im (x)*re(x)/ + (5 + re(x))*\1 + 12*im (x) + 12*re (x) - 72*im (x)*re (x) + re(x)/ + I*\-1 - re(x) - 12*im (x) - 12*re (x) + (5 + re(x))*\1 + 48*re (x) - 48*im (x)*re(x)/ + 72*im (x)*re (x)/*im(x)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
(5 + re(x)) + im (x)
$$\frac{\left(\operatorname{re}{\left(x\right)} + 5\right) \left(12 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} + \operatorname{re}{\left(x\right)} + 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 1\right) + \left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right) \left(\operatorname{im}{\left(x\right)}\right)^{2} + i \left(\left(\operatorname{re}{\left(x\right)} + 5\right) \left(48 \left(\operatorname{re}{\left(x\right)}\right)^{3} - 48 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{2} + 1\right) - 12 \left(\operatorname{re}{\left(x\right)}\right)^{4} + 72 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - \operatorname{re}{\left(x\right)} - 12 \left(\operatorname{im}{\left(x\right)}\right)^{4} - 1\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 5\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
(im(x)^2*(1 + 48*re(x)^3 - 48*im(x)^2*re(x)) + (5 + re(x))*(1 + 12*im(x)^4 + 12*re(x)^4 - 72*im(x)^2*re(x)^2 + re(x)) + i*(-1 - re(x) - 12*im(x)^4 - 12*re(x)^4 + (5 + re(x))*(1 + 48*re(x)^3 - 48*im(x)^2*re(x)) + 72*im(x)^2*re(x)^2)*im(x))/((5 + re(x))^2 + im(x)^2)