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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
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Expresiones idénticas
- xy²= quinientos treinta y nueve (y+ uno)
- xy² es igual a 539(y más 1)
- xy² es igual a quinientos treinta y nueve (y más uno)
- xy²=539y+1
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Expresiones semejantes
- xy²=539(y-1)
- (x²+y²)^cos(x*y)+arctang(x*y²)=z
xy²=539(y+1) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos una ecuación lineal:
Abrimos los paréntesis en el miembro derecho de la ecuación
Dividamos ambos miembros de la ecuación en y^2
Obtenemos la respuesta: x = 539*(1 + y)/y^2
x*y^2 = 539*(y+1)
Abrimos los paréntesis en el miembro derecho de la ecuación
x*y^2 = 539*y+539*1
Dividamos ambos miembros de la ecuación en y^2
x = 539 + 539*y / (y^2)
Obtenemos la respuesta: x = 539*(1 + y)/y^2
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$x y^{2} = 539 y + 539$$
Коэффициент при x равен
$$y^{2}$$
entonces son posibles los casos para y :
$$y < 0$$
$$y = 0$$
Consideremos todos los casos con detalles:
Con
$$y < 0$$
la ecuación será
$$x = 0$$
su solución
$$x = 0$$
Con
$$y = 0$$
la ecuación será
$$-539 = 0$$
su solución
no hay soluciones
$$x y^{2} = 539 y + 539$$
Коэффициент при x равен
$$y^{2}$$
entonces son posibles los casos para y :
$$y < 0$$
$$y = 0$$
Consideremos todos los casos con detalles:
Con
$$y < 0$$
la ecuación será
$$x = 0$$
su solución
$$x = 0$$
Con
$$y = 0$$
la ecuación será
$$-539 = 0$$
su solución
no hay soluciones
Gráfica
Respuesta rápida
[src]
// 2 2 \ \ / 2 2 \ 2
|| 539*im (y) 539*re (y) | 1078*(1 + re(y))*im(y)*re(y)| | 539*im (y) 539*re (y) | 1078*im (y)*re(y)
x1 = I*||- ------------------ + ------------------|*im(y) - ----------------------------| + (1 + re(y))*|- ------------------ + ------------------| + ------------------
|| 2 2| 2 | | 2 2| 2
|| / 2 2 \ / 2 2 \ | / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \
\\ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ / \ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/
$$x_{1} = i \left(\left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \operatorname{im}{\left(y\right)} - \frac{1078 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\operatorname{re}{\left(y\right)} + 1\right) + \frac{1078 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
x1 = i*((539*re(y)^2/(re(y)^2 + im(y)^2)^2 - 539*im(y)^2/(re(y)^2 + im(y)^2)^2)*im(y) - 1078*(re(y) + 1)*re(y)*im(y)/(re(y)^2 + im(y)^2)^2) + (539*re(y)^2/(re(y)^2 + im(y)^2)^2 - 539*im(y)^2/(re(y)^2 + im(y)^2)^2)*(re(y) + 1) + 1078*re(y)*im(y)^2/(re(y)^2 + im(y)^2)^2
Suma y producto de raíces
[src]
suma
// 2 2 \ \ / 2 2 \ 2 || 539*im (y) 539*re (y) | 1078*(1 + re(y))*im(y)*re(y)| | 539*im (y) 539*re (y) | 1078*im (y)*re(y) I*||- ------------------ + ------------------|*im(y) - ----------------------------| + (1 + re(y))*|- ------------------ + ------------------| + ------------------ || 2 2| 2 | | 2 2| 2 || / 2 2 \ / 2 2 \ | / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \ \\ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ / \ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/
$$i \left(\left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \operatorname{im}{\left(y\right)} - \frac{1078 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\operatorname{re}{\left(y\right)} + 1\right) + \frac{1078 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
=
// 2 2 \ \ / 2 2 \ 2 || 539*im (y) 539*re (y) | 1078*(1 + re(y))*im(y)*re(y)| | 539*im (y) 539*re (y) | 1078*im (y)*re(y) I*||- ------------------ + ------------------|*im(y) - ----------------------------| + (1 + re(y))*|- ------------------ + ------------------| + ------------------ || 2 2| 2 | | 2 2| 2 || / 2 2 \ / 2 2 \ | / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \ \\ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ / \ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/
$$i \left(\left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \operatorname{im}{\left(y\right)} - \frac{1078 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\operatorname{re}{\left(y\right)} + 1\right) + \frac{1078 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
producto
// 2 2 \ \ / 2 2 \ 2 || 539*im (y) 539*re (y) | 1078*(1 + re(y))*im(y)*re(y)| | 539*im (y) 539*re (y) | 1078*im (y)*re(y) I*||- ------------------ + ------------------|*im(y) - ----------------------------| + (1 + re(y))*|- ------------------ + ------------------| + ------------------ || 2 2| 2 | | 2 2| 2 || / 2 2 \ / 2 2 \ | / 2 2 \ | | / 2 2 \ / 2 2 \ | / 2 2 \ \\ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ / \ \im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/
$$i \left(\left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \operatorname{im}{\left(y\right)} - \frac{1078 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \left(\frac{539 \left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{539 \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\operatorname{re}{\left(y\right)} + 1\right) + \frac{1078 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
=
/ / 2 2 \ 2 / 2 2 \ \
539*\(1 + re(y))*\re (y) - im (y)/ + 2*im (y)*re(y) + I*\re (y) - im (y) - 2*(1 + re(y))*re(y)/*im(y)/
------------------------------------------------------------------------------------------------------
2
/ 2 2 \
\im (y) + re (y)/
$$\frac{539 \left(\left(\operatorname{re}{\left(y\right)} + 1\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) + i \left(- 2 \left(\operatorname{re}{\left(y\right)} + 1\right) \operatorname{re}{\left(y\right)} + \left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
539*((1 + re(y))*(re(y)^2 - im(y)^2) + 2*im(y)^2*re(y) + i*(re(y)^2 - im(y)^2 - 2*(1 + re(y))*re(y))*im(y))/(im(y)^2 + re(y)^2)^2