Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 8*x-3*(2*x+1)=2*x+4
-
Ecuación x^3=27
-
Ecuación 1+sin(x)=0
-
Ecuación 2*x^2+6*x+9=
- Expresar {x} en función de y en la ecuación:
- 20*x+6*y=8
- -11*x-15*y=14
- -11*x+10*y=-9
- 6*x-2*y=20
-
Expresiones idénticas
- xy^ tres +y^ dos = uno
- xy al cubo más y al cuadrado es igual a 1
- xy en el grado tres más y en el grado dos es igual a uno
- xy3+y2=1
- xy³+y²=1
- xy en el grado 3+y en el grado 2=1
-
Expresiones semejantes
- xy^3-y^2=1
-
Expresiones con funciones
- xy
- xy+lny-2cosx=0
- xy+ln(y)=1
- xy+e^(x+y)+4=0
- xy-y^2
- xy-2x+4y=25
xy^3+y^2=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 (y^2 + x*y^3)/x
Obtenemos la respuesta: x = (1 - y^2)/y^3
x*y^3+y^2 = 1
Dividamos ambos miembros de la ecuación en (y^2 + x*y^3)/x
x = 1 / ((y^2 + x*y^3)/x)
Obtenemos la respuesta: x = (1 - y^2)/y^3
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$x y^{3} + y^{2} = 1$$
Коэффициент при x равен
$$y^{3}$$
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
$$-1 = 0$$
su solución
no hay soluciones
$$x y^{3} + y^{2} = 1$$
Коэффициент при x равен
$$y^{3}$$
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
$$-1 = 0$$
su solución
no hay soluciones
Gráfica
Suma y producto de raíces
[src]
suma
// 3 2 \ / 3 2 \ \ / 3 2 \ / 3 2 \ || im (y) 3*re (y)*im(y) | / 2 2 \ | re (y) 3*im (y)*re(y) | | | re (y) 3*im (y)*re(y) | / 2 2 \ | im (y) 3*re (y)*im(y) | I*||------------------ - ------------------|*\1 + im (y) - re (y)/ - 2*|------------------ - ------------------|*im(y)*re(y)| + |------------------ - ------------------|*\1 + im (y) - re (y)/ + 2*|------------------ - ------------------|*im(y)*re(y) || 3 3| | 3 3| | | 3 3| | 3 3| ||/ 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)/ / \\im (y) + re (y)/ \im (y) + re (y)/ /
$$\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} - \frac{3 \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)^{3}}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) + i \left(- 2 \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} - \frac{3 \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)^{3}}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \left(- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)\right) + 2 \left(- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}$$
=
// 3 2 \ / 3 2 \ \ / 3 2 \ / 3 2 \ || im (y) 3*re (y)*im(y) | / 2 2 \ | re (y) 3*im (y)*re(y) | | | re (y) 3*im (y)*re(y) | / 2 2 \ | im (y) 3*re (y)*im(y) | I*||------------------ - ------------------|*\1 + im (y) - re (y)/ - 2*|------------------ - ------------------|*im(y)*re(y)| + |------------------ - ------------------|*\1 + im (y) - re (y)/ + 2*|------------------ - ------------------|*im(y)*re(y) || 3 3| | 3 3| | | 3 3| | 3 3| ||/ 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)/ / \\im (y) + re (y)/ \im (y) + re (y)/ /
$$\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} - \frac{3 \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)^{3}}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) + i \left(- 2 \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} - \frac{3 \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)^{3}}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \left(- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)\right) + 2 \left(- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}$$
producto
// 3 2 \ / 3 2 \ \ / 3 2 \ / 3 2 \ || im (y) 3*re (y)*im(y) | / 2 2 \ | re (y) 3*im (y)*re(y) | | | re (y) 3*im (y)*re(y) | / 2 2 \ | im (y) 3*re (y)*im(y) | I*||------------------ - ------------------|*\1 + im (y) - re (y)/ - 2*|------------------ - ------------------|*im(y)*re(y)| + |------------------ - ------------------|*\1 + im (y) - re (y)/ + 2*|------------------ - ------------------|*im(y)*re(y) || 3 3| | 3 3| | | 3 3| | 3 3| ||/ 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)/ / \\im (y) + re (y)/ \im (y) + re (y)/ /
$$\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} - \frac{3 \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)^{3}}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) + i \left(- 2 \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} - \frac{3 \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)^{3}}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \left(- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)\right) + 2 \left(- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}$$
=
/ 2 / 2 2 \ / 2 2 \ / 2 2 \\ / 2 2 \ / 2 2 \ 2 / 2 2 \
I*\re (y)*\- 2*re (y) + 6*im (y)/ - \- im (y) + 3*re (y)/*\1 + im (y) - re (y)//*im(y) + \re (y) - 3*im (y)/*\1 + im (y) - re (y)/*re(y) - 2*im (y)*\- im (y) + 3*re (y)/*re(y)
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
/ 2 2 \
\im (y) + re (y)/
$$\frac{i \left(\left(- 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 6 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)\right) \operatorname{im}{\left(y\right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - 3 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \operatorname{re}{\left(y\right)} - 2 \left(3 \left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}}$$
(i*(re(y)^2*(-2*re(y)^2 + 6*im(y)^2) - (-im(y)^2 + 3*re(y)^2)*(1 + im(y)^2 - re(y)^2))*im(y) + (re(y)^2 - 3*im(y)^2)*(1 + im(y)^2 - re(y)^2)*re(y) - 2*im(y)^2*(-im(y)^2 + 3*re(y)^2)*re(y))/(im(y)^2 + re(y)^2)^3
Respuesta rápida
[src]
// 3 2 \ / 3 2 \ \ / 3 2 \ / 3 2 \
|| im (y) 3*re (y)*im(y) | / 2 2 \ | re (y) 3*im (y)*re(y) | | | re (y) 3*im (y)*re(y) | / 2 2 \ | im (y) 3*re (y)*im(y) |
x1 = I*||------------------ - ------------------|*\1 + im (y) - re (y)/ - 2*|------------------ - ------------------|*im(y)*re(y)| + |------------------ - ------------------|*\1 + im (y) - re (y)/ + 2*|------------------ - ------------------|*im(y)*re(y)
|| 3 3| | 3 3| | | 3 3| | 3 3|
||/ 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)/ / \\im (y) + re (y)/ \im (y) + re (y)/ /
$$x_{1} = \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} - \frac{3 \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)^{3}}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) + i \left(- 2 \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} - \frac{3 \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)^{3}}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \left(- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}}\right) \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)\right) + 2 \left(- \frac{3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}} + \frac{\left(\operatorname{im}{\left(y\right)}\right)^{3}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{3}}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}$$
x1 = (re(y)^3/(re(y)^2 + im(y)^2)^3 - 3*re(y)*im(y)^2/(re(y)^2 + im(y)^2)^3)*(-re(y)^2 + im(y)^2 + 1) + i*(-2*(re(y)^3/(re(y)^2 + im(y)^2)^3 - 3*re(y)*im(y)^2/(re(y)^2 + im(y)^2)^3)*re(y)*im(y) + (-3*re(y)^2*im(y)/(re(y)^2 + im(y)^2)^3 + im(y)^3/(re(y)^2 + im(y)^2)^3)*(-re(y)^2 + im(y)^2 + 1)) + 2*(-3*re(y)^2*im(y)/(re(y)^2 + im(y)^2)^3 + im(y)^3/(re(y)^2 + im(y)^2)^3)*re(y)*im(y)