Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$- x \left(10 + \frac{25}{p}\right) - 60 x = -120 + \frac{60}{p}$$
Коэффициент при x равен
$$-70 - \frac{25}{p}$$
entonces son posibles los casos para p :
$$p < - \frac{5}{14}$$
$$p = - \frac{5}{14}$$
Consideremos todos los casos con detalles:
Con
$$p < - \frac{5}{14}$$
la ecuación será
$$\frac{3120}{19} - \frac{980 x}{19} = 0$$
su solución
$$x = \frac{156}{49}$$
Con
$$p = - \frac{5}{14}$$
la ecuación será
$$288 = 0$$
su solución
no hay soluciones
Suma y producto de raíces
[src]
2
/ 168*(-1 + 2*re(p))*im(p) 24*(5 + 14*re(p))*im(p) \ 336*im (p) 12*(-1 + 2*re(p))*(5 + 14*re(p))
I*|- ---------------------------- + ----------------------------| + ---------------------------- + --------------------------------
| 2 2 2 2 | 2 2 2 2
\ (5 + 14*re(p)) + 196*im (p) (5 + 14*re(p)) + 196*im (p)/ (5 + 14*re(p)) + 196*im (p) (5 + 14*re(p)) + 196*im (p)
$$i \left(- \frac{168 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{24 \left(14 \operatorname{re}{\left(p\right)} + 5\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}\right) + \frac{12 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{336 \left(\operatorname{im}{\left(p\right)}\right)^{2}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$
2
/ 168*(-1 + 2*re(p))*im(p) 24*(5 + 14*re(p))*im(p) \ 336*im (p) 12*(-1 + 2*re(p))*(5 + 14*re(p))
I*|- ---------------------------- + ----------------------------| + ---------------------------- + --------------------------------
| 2 2 2 2 | 2 2 2 2
\ (5 + 14*re(p)) + 196*im (p) (5 + 14*re(p)) + 196*im (p)/ (5 + 14*re(p)) + 196*im (p) (5 + 14*re(p)) + 196*im (p)
$$i \left(- \frac{168 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{24 \left(14 \operatorname{re}{\left(p\right)} + 5\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}\right) + \frac{12 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{336 \left(\operatorname{im}{\left(p\right)}\right)^{2}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$
2
/ 168*(-1 + 2*re(p))*im(p) 24*(5 + 14*re(p))*im(p) \ 336*im (p) 12*(-1 + 2*re(p))*(5 + 14*re(p))
I*|- ---------------------------- + ----------------------------| + ---------------------------- + --------------------------------
| 2 2 2 2 | 2 2 2 2
\ (5 + 14*re(p)) + 196*im (p) (5 + 14*re(p)) + 196*im (p)/ (5 + 14*re(p)) + 196*im (p) (5 + 14*re(p)) + 196*im (p)
$$i \left(- \frac{168 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{24 \left(14 \operatorname{re}{\left(p\right)} + 5\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}\right) + \frac{12 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{336 \left(\operatorname{im}{\left(p\right)}\right)^{2}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$
/ 2 \
12*\28*im (p) + (-1 + 2*re(p))*(5 + 14*re(p)) + 24*I*im(p)/
-----------------------------------------------------------
2 2
(5 + 14*re(p)) + 196*im (p)
$$\frac{12 \left(\left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right) + 28 \left(\operatorname{im}{\left(p\right)}\right)^{2} + 24 i \operatorname{im}{\left(p\right)}\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$
12*(28*im(p)^2 + (-1 + 2*re(p))*(5 + 14*re(p)) + 24*i*im(p))/((5 + 14*re(p))^2 + 196*im(p)^2)
2
/ 168*(-1 + 2*re(p))*im(p) 24*(5 + 14*re(p))*im(p) \ 336*im (p) 12*(-1 + 2*re(p))*(5 + 14*re(p))
x1 = I*|- ---------------------------- + ----------------------------| + ---------------------------- + --------------------------------
| 2 2 2 2 | 2 2 2 2
\ (5 + 14*re(p)) + 196*im (p) (5 + 14*re(p)) + 196*im (p)/ (5 + 14*re(p)) + 196*im (p) (5 + 14*re(p)) + 196*im (p)
$$x_{1} = i \left(- \frac{168 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{24 \left(14 \operatorname{re}{\left(p\right)} + 5\right) \operatorname{im}{\left(p\right)}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}\right) + \frac{12 \left(2 \operatorname{re}{\left(p\right)} - 1\right) \left(14 \operatorname{re}{\left(p\right)} + 5\right)}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}} + \frac{336 \left(\operatorname{im}{\left(p\right)}\right)^{2}}{\left(14 \operatorname{re}{\left(p\right)} + 5\right)^{2} + 196 \left(\operatorname{im}{\left(p\right)}\right)^{2}}$$
x1 = i*(-168*(2*re(p) - 1)*im(p)/((14*re(p) + 5)^2 + 196*im(p)^2) + 24*(14*re(p) + 5)*im(p)/((14*re(p) + 5)^2 + 196*im(p)^2)) + 12*(2*re(p) - 1)*(14*re(p) + 5)/((14*re(p) + 5)^2 + 196*im(p)^2) + 336*im(p)^2/((14*re(p) + 5)^2 + 196*im(p)^2)