c*x=c+6 (уравнение)

Найду корень уравнения: c*x=c+6

Вы ввели

c*x = c + 6

$$c x = c + 6$$

Подробное решение

Дано линейное уравнение:

c*x = c+6

Разделим обе части ур-ния на c

x = 6 + c / (c)

Получим ответ: x = (6 + c)/c

Быстрый ответ

                                                      2                           
       /  im(c)*re(c)     (6 + re(c))*im(c)\        im (c)       (6 + re(c))*re(c)
x1 = I*|--------------- - -----------------| + --------------- + -----------------
       |  2        2         2        2    |     2        2         2        2    
       \im (c) + re (c)    im (c) + re (c) /   im (c) + re (c)    im (c) + re (c) 

$$x_{1} = i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + 6\right) \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + 6\right) \operatorname{re}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$

Сумма и произведение корней

сумма

                                                 2                           
  /  im(c)*re(c)     (6 + re(c))*im(c)\        im (c)       (6 + re(c))*re(c)
I*|--------------- - -----------------| + --------------- + -----------------
  |  2        2         2        2    |     2        2         2        2    
  \im (c) + re (c)    im (c) + re (c) /   im (c) + re (c)    im (c) + re (c) 

$$i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + 6\right) \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + 6\right) \operatorname{re}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$

=

                                                 2                           
  /  im(c)*re(c)     (6 + re(c))*im(c)\        im (c)       (6 + re(c))*re(c)
I*|--------------- - -----------------| + --------------- + -----------------
  |  2        2         2        2    |     2        2         2        2    
  \im (c) + re (c)    im (c) + re (c) /   im (c) + re (c)    im (c) + re (c) 

$$i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + 6\right) \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + 6\right) \operatorname{re}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$

произведение

                                                 2                           
  /  im(c)*re(c)     (6 + re(c))*im(c)\        im (c)       (6 + re(c))*re(c)
I*|--------------- - -----------------| + --------------- + -----------------
  |  2        2         2        2    |     2        2         2        2    
  \im (c) + re (c)    im (c) + re (c) /   im (c) + re (c)    im (c) + re (c) 

$$i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + 6\right) \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\operatorname{re}{\left(c\right)} \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + 6\right) \operatorname{re}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)}\right)^{2}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$

=

  2                                   
im (c) + (6 + re(c))*re(c) - 6*I*im(c)
--------------------------------------
             2        2               
           im (c) + re (c)            

$$\frac{\left(\operatorname{re}{\left(c\right)} + 6\right) \operatorname{re}{\left(c\right)} + \left(\operatorname{im}{\left(c\right)}\right)^{2} - 6 i \operatorname{im}{\left(c\right)}}{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}}$$

Решение параметрического уравнения

Дано уравнение с параметром:
$$c x = c + 6$$
Коэффициент при x равен
$$c$$
тогда возможные случаи для c :
$$c < 0$$
$$c = 0$$
Рассмотри все случаи подробнее:
При
$$c < 0$$
уравнение будет
$$- x - 5 = 0$$
его решение
$$x = -5$$
При
$$c = 0$$
уравнение будет
$$-6 = 0$$
его решение
нет решений