x/(-b+c)=d (уравнение)

Найду корень уравнения: x/(-b+c)=d

Вы ввели

  x       
------ = d
-b + c    

$$\frac{x}{- b + c} = d$$

Быстрый ответ

x1 = I*((-im(b) + im(c))*re(d) + (-re(b) + re(c))*im(d)) + (-re(b) + re(c))*re(d) - (-im(b) + im(c))*im(d)

$$x_{1} = i \left(\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(d\right)} + \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(d\right)}\right) + \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(d\right)} - \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(d\right)}$$

Сумма и произведение корней

сумма

I*((-im(b) + im(c))*re(d) + (-re(b) + re(c))*im(d)) + (-re(b) + re(c))*re(d) - (-im(b) + im(c))*im(d)

$$i \left(\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(d\right)} + \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(d\right)}\right) + \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(d\right)} - \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(d\right)}$$

=

I*((-im(b) + im(c))*re(d) + (-re(b) + re(c))*im(d)) + (-re(b) + re(c))*re(d) - (-im(b) + im(c))*im(d)

$$i \left(\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(d\right)} + \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(d\right)}\right) + \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(d\right)} - \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(d\right)}$$

произведение

I*((-im(b) + im(c))*re(d) + (-re(b) + re(c))*im(d)) + (-re(b) + re(c))*re(d) - (-im(b) + im(c))*im(d)

$$i \left(\left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(d\right)} + \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(d\right)}\right) + \left(- \operatorname{re}{\left(b\right)} + \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(d\right)} - \left(- \operatorname{im}{\left(b\right)} + \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(d\right)}$$

=

(-im(c) + im(b))*im(d) - I*((-im(c) + im(b))*re(d) + (-re(c) + re(b))*im(d)) - (-re(c) + re(b))*re(d)

$$- i \left(\left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(c\right)}\right) \operatorname{im}{\left(d\right)} + \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(c\right)}\right) \operatorname{re}{\left(d\right)}\right) - \left(\operatorname{re}{\left(b\right)} - \operatorname{re}{\left(c\right)}\right) \operatorname{re}{\left(d\right)} + \left(\operatorname{im}{\left(b\right)} - \operatorname{im}{\left(c\right)}\right) \operatorname{im}{\left(d\right)}$$

Решение параметрического уравнения

Дано уравнение с параметром:
$$\frac{x}{- b + c} = d$$
Коэффициент при x равен
$$\frac{1}{- b + c}$$
тогда возможные случаи для b :
Рассмотри все случаи подробнее: