Solución detallada
Tenemos una ecuación lineal:
a*x+b*y-82/9 = 0
Transportamos los términos libres (sin x)
del miembro izquierdo al derecho, obtenemos:
$$a x + b y = \frac{82}{9}$$
Dividamos ambos miembros de la ecuación en (a*x + b*y)/x
x = 82/9 / ((a*x + b*y)/x)
Obtenemos la respuesta: x = (82/9 - b*y)/a
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x + b y - \frac{82}{9} = 0$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$b y - x - \frac{82}{9} = 0$$
su solución
$$x = b y - \frac{82}{9}$$
Con
$$a = 0$$
la ecuación será
$$b y - \frac{82}{9} = 0$$
su solución
Suma y producto de raíces
[src]
/ (82/9 - re(b*y))*im(a) im(b*y)*re(a) \ (82/9 - re(b*y))*re(a) im(a)*im(b*y)
I*|- ---------------------- - ---------------| + ---------------------- - ---------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a)/ im (a) + re (a) im (a) + re (a)
$$\frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(- \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
/ (82/9 - re(b*y))*im(a) im(b*y)*re(a) \ (82/9 - re(b*y))*re(a) im(a)*im(b*y)
I*|- ---------------------- - ---------------| + ---------------------- - ---------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a)/ im (a) + re (a) im (a) + re (a)
$$\frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(- \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
/ (82/9 - re(b*y))*im(a) im(b*y)*re(a) \ (82/9 - re(b*y))*re(a) im(a)*im(b*y)
I*|- ---------------------- - ---------------| + ---------------------- - ---------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a)/ im (a) + re (a) im (a) + re (a)
$$\frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(- \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(-82 + 9*re(b*y))*re(a) I*((-82 + 9*re(b*y))*im(a) - 9*im(b*y)*re(a))
-im(a)*im(b*y) - ----------------------- + ---------------------------------------------
9 9
----------------------------------------------------------------------------------------
2 2
im (a) + re (a)
$$\frac{\frac{i \left(\left(9 \operatorname{re}{\left(b y\right)} - 82\right) \operatorname{im}{\left(a\right)} - 9 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}\right)}{9} - \frac{\left(9 \operatorname{re}{\left(b y\right)} - 82\right) \operatorname{re}{\left(a\right)}}{9} - \operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(-im(a)*im(b*y) - (-82 + 9*re(b*y))*re(a)/9 + i*((-82 + 9*re(b*y))*im(a) - 9*im(b*y)*re(a))/9)/(im(a)^2 + re(a)^2)
/ (82/9 - re(b*y))*im(a) im(b*y)*re(a) \ (82/9 - re(b*y))*re(a) im(a)*im(b*y)
x1 = I*|- ---------------------- - ---------------| + ---------------------- - ---------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a)/ im (a) + re (a) im (a) + re (a)
$$x_{1} = \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(- \frac{\left(\frac{82}{9} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\operatorname{re}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) - \frac{\operatorname{im}{\left(a\right)} \operatorname{im}{\left(b y\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x1 = (82/9 - re(b*y))*re(a)/(re(a)^2 + im(a)^2) + i*(-(82/9 - re(b*y))*im(a)/(re(a)^2 + im(a)^2) - re(a)*im(b*y)/(re(a)^2 + im(a)^2)) - im(a)*im(b*y)/(re(a)^2 + im(a)^2)