Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$x y + y = 5$$
Коэффициент при y равен
$$x + 1$$
entonces son posibles los casos para x :
$$x < -1$$
$$x = -1$$
Consideremos todos los casos con detalles:
Con
$$x < -1$$
la ecuación será
$$- y - 5 = 0$$
su solución
$$y = -5$$
Con
$$x = -1$$
la ecuación será
$$-5 = 0$$
su solución
no hay soluciones
Suma y producto de raíces
[src]
5*(1 + re(x)) 5*I*im(x)
--------------------- - ---------------------
2 2 2 2
(1 + re(x)) + im (x) (1 + re(x)) + im (x)
$$\frac{5 \left(\operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{5 i \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
5*(1 + re(x)) 5*I*im(x)
--------------------- - ---------------------
2 2 2 2
(1 + re(x)) + im (x) (1 + re(x)) + im (x)
$$\frac{5 \left(\operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{5 i \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
5*(1 + re(x)) 5*I*im(x)
--------------------- - ---------------------
2 2 2 2
(1 + re(x)) + im (x) (1 + re(x)) + im (x)
$$\frac{5 \left(\operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{5 i \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
5*(1 - I*im(x) + re(x))
-----------------------
2 2
(1 + re(x)) + im (x)
$$\frac{5 \left(\operatorname{re}{\left(x\right)} - i \operatorname{im}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
5*(1 - i*im(x) + re(x))/((1 + re(x))^2 + im(x)^2)
5*(1 + re(x)) 5*I*im(x)
y1 = --------------------- - ---------------------
2 2 2 2
(1 + re(x)) + im (x) (1 + re(x)) + im (x)
$$y_{1} = \frac{5 \left(\operatorname{re}{\left(x\right)} + 1\right)}{\left(\operatorname{re}{\left(x\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{5 i \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} + 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
y1 = 5*(re(x) + 1)/((re(x) + 1)^2 + im(x)^2) - 5*i*im(x)/((re(x) + 1)^2 + im(x)^2)