x^36=6 (уравнение)

Найду корень уравнения: x^36=6

Вы ввели

 36    
x   = 6

$$x^{36} = 6$$

Подробное решение

Дано уравнение
$$x^{36} = 6$$
Т.к. степень в ур-нии равна = 36 - содержит чётное число 36 в числителе, то
ур-ние будет иметь два действительных корня.
Извлечём корень 36-й степени из обеих частей ур-ния:
Получим:
$$\sqrt[36]{x^{36}} = \sqrt[36]{6}$$
$$\sqrt[36]{x^{36}} = -1 \sqrt[36]{6}$$
или
$$x = \sqrt[36]{6}$$
$$x = - \sqrt[36]{6}$$
Раскрываем скобочки в правой части ур-ния

x = 6^1/36

Получим ответ: x = 6^(1/36)
Раскрываем скобочки в правой части ур-ния

x = -6^1/36

Получим ответ: x = -6^(1/36)
или
$$x_{1} = - \sqrt[36]{6}$$
$$x_{2} = \sqrt[36]{6}$$

Остальные 34 корня(ей) являются комплексными.
сделаем замену:
$$z = x$$
тогда ур-ние будет таким:
$$z^{36} = 6$$
Любое комплексное число можно представить так:
$$z = r e^{i p}$$
подставляем в уравнение
$$r^{36} e^{36 i p} = 6$$
где
$$r = \sqrt[36]{6}$$
- модуль комплексного числа
Подставляем r:
$$e^{36 i p} = 1$$
Используя формулу Эйлера, найдём корни для p
$$i \sin{\left (36 p \right )} + \cos{\left (36 p \right )} = 1$$
значит
$$\cos{\left (36 p \right )} = 1$$
и
$$\sin{\left (36 p \right )} = 0$$
тогда
$$p = \frac{\pi N}{18}$$
где N=0,1,2,3,...
Перебирая значения N и подставив p в формулу для z
Значит, решением будет для z:
$$z_{1} = - \sqrt[36]{6}$$
$$z_{2} = \sqrt[36]{6}$$
$$z_{3} = - \sqrt[36]{6} i$$
$$z_{4} = \sqrt[36]{6} i$$
$$z_{5} = - \frac{\sqrt[36]{6}}{2} - \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$
$$z_{6} = - \frac{\sqrt[36]{6}}{2} + \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$
$$z_{7} = \frac{\sqrt[36]{6}}{2} - \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$
$$z_{8} = \frac{\sqrt[36]{6}}{2} + \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$
$$z_{9} = - \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} - \frac{\sqrt[36]{6} i}{2}$$
$$z_{10} = - \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} + \frac{\sqrt[36]{6} i}{2}$$
$$z_{11} = \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} - \frac{\sqrt[36]{6} i}{2}$$
$$z_{12} = \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} + \frac{\sqrt[36]{6} i}{2}$$
$$z_{13} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$
$$z_{14} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$
$$z_{15} = \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$
$$z_{16} = \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$
$$z_{17} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$
$$z_{18} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$
$$z_{19} = \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$
$$z_{20} = \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$
$$z_{21} = - \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$
$$z_{22} = - \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$
$$z_{23} = \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$
$$z_{24} = \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$
$$z_{25} = - \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$
$$z_{26} = - \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$
$$z_{27} = \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$
$$z_{28} = \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$
$$z_{29} = - \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$
$$z_{30} = - \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$
$$z_{31} = \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$
$$z_{32} = \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$
$$z_{33} = - \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$
$$z_{34} = - \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$
$$z_{35} = \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$
$$z_{36} = \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$
делаем обратную замену
$$z = x$$
$$x = z$$

Тогда, окончательный ответ:
$$x_{1} = - \sqrt[36]{6}$$
$$x_{2} = \sqrt[36]{6}$$
$$x_{3} = - \sqrt[36]{6} i$$
$$x_{4} = \sqrt[36]{6} i$$
$$x_{5} = - \frac{\sqrt[36]{6}}{2} - \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$
$$x_{6} = - \frac{\sqrt[36]{6}}{2} + \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$
$$x_{7} = \frac{\sqrt[36]{6}}{2} - \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$
$$x_{8} = \frac{\sqrt[36]{6}}{2} + \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$
$$x_{9} = - \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} - \frac{\sqrt[36]{6} i}{2}$$
$$x_{10} = - \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} + \frac{\sqrt[36]{6} i}{2}$$
$$x_{11} = \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} - \frac{\sqrt[36]{6} i}{2}$$
$$x_{12} = \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} + \frac{\sqrt[36]{6} i}{2}$$
$$x_{13} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$
$$x_{14} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$
$$x_{15} = \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$
$$x_{16} = \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$
$$x_{17} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$
$$x_{18} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$
$$x_{19} = \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$
$$x_{20} = \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$
$$x_{21} = - \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$
$$x_{22} = - \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$
$$x_{23} = \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$
$$x_{24} = \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$
$$x_{25} = - \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$
$$x_{26} = - \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$
$$x_{27} = \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$
$$x_{28} = \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$
$$x_{29} = - \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$
$$x_{30} = - \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$
$$x_{31} = \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$
$$x_{32} = \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$
$$x_{33} = - \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$
$$x_{34} = - \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$
$$x_{35} = \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$
$$x_{36} = \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$

Быстрый ответ

      36___
x1 = -\/ 6 

$$x_{1} = - \sqrt[36]{6}$$

     36___
x2 = \/ 6 

$$x_{2} = \sqrt[36]{6}$$

        36___
x3 = -I*\/ 6 

$$x_{3} = - \sqrt[36]{6} i$$

       36___
x4 = I*\/ 6 

$$x_{4} = \sqrt[36]{6} i$$

                        19
                        --
       36___     36___  36
       \/ 6    I*\/ 2 *3  
x5 = - ----- - -----------
         2          2     

$$x_{5} = - \frac{\sqrt[36]{6}}{2} - \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$

                        19
                        --
       36___     36___  36
       \/ 6    I*\/ 2 *3  
x6 = - ----- + -----------
         2          2     

$$x_{6} = - \frac{\sqrt[36]{6}}{2} + \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$

                      19
                      --
     36___     36___  36
     \/ 6    I*\/ 2 *3  
x7 = ----- - -----------
       2          2     

$$x_{7} = \frac{\sqrt[36]{6}}{2} - \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$

                      19
                      --
     36___     36___  36
     \/ 6    I*\/ 2 *3  
x8 = ----- + -----------
       2          2     

$$x_{8} = \frac{\sqrt[36]{6}}{2} + \frac{\sqrt[36]{2} i}{2} 3^{\frac{19}{36}}$$

                        19
                        --
         36___   36___  36
       I*\/ 6    \/ 2 *3  
x9 = - ------- - ---------
          2          2    

$$x_{9} = - \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} - \frac{\sqrt[36]{6} i}{2}$$

                       19
                       --
        36___   36___  36
      I*\/ 6    \/ 2 *3  
x10 = ------- - ---------
         2          2    

$$x_{10} = - \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} + \frac{\sqrt[36]{6} i}{2}$$

             19          
             --          
      36___  36     36___
      \/ 2 *3     I*\/ 6 
x11 = --------- - -------
          2          2   

$$x_{11} = \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} - \frac{\sqrt[36]{6} i}{2}$$

                       19
                       --
        36___   36___  36
      I*\/ 6    \/ 2 *3  
x12 = ------- + ---------
         2          2    

$$x_{12} = \frac{\sqrt[36]{2}}{2} 3^{\frac{19}{36}} + \frac{\sqrt[36]{6} i}{2}$$

        36___    /pi\     36___    /pi\
x13 = - \/ 6 *cos|--| - I*\/ 6 *sin|--|
                 \18/              \18/

$$x_{13} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$

        36___    /pi\     36___    /pi\
x14 = - \/ 6 *cos|--| + I*\/ 6 *sin|--|
                 \18/              \18/

$$x_{14} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$

      36___    /pi\     36___    /pi\
x15 = \/ 6 *cos|--| - I*\/ 6 *sin|--|
               \18/              \18/

$$x_{15} = \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$

      36___    /pi\     36___    /pi\
x16 = \/ 6 *cos|--| + I*\/ 6 *sin|--|
               \18/              \18/

$$x_{16} = \sqrt[36]{6} \cos{\left (\frac{\pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{18} \right )}$$

        36___    /pi\     36___    /pi\
x17 = - \/ 6 *cos|--| - I*\/ 6 *sin|--|
                 \9 /              \9 /

$$x_{17} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$

        36___    /pi\     36___    /pi\
x18 = - \/ 6 *cos|--| + I*\/ 6 *sin|--|
                 \9 /              \9 /

$$x_{18} = - \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$

      36___    /pi\     36___    /pi\
x19 = \/ 6 *cos|--| - I*\/ 6 *sin|--|
               \9 /              \9 /

$$x_{19} = \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$

      36___    /pi\     36___    /pi\
x20 = \/ 6 *cos|--| + I*\/ 6 *sin|--|
               \9 /              \9 /

$$x_{20} = \sqrt[36]{6} \cos{\left (\frac{\pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{\pi}{9} \right )}$$

        36___    /2*pi\     36___    /2*pi\
x21 = - \/ 6 *cos|----| - I*\/ 6 *sin|----|
                 \ 9  /              \ 9  /

$$x_{21} = - \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$

        36___    /2*pi\     36___    /2*pi\
x22 = - \/ 6 *cos|----| + I*\/ 6 *sin|----|
                 \ 9  /              \ 9  /

$$x_{22} = - \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$

      36___    /2*pi\     36___    /2*pi\
x23 = \/ 6 *cos|----| - I*\/ 6 *sin|----|
               \ 9  /              \ 9  /

$$x_{23} = \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$

      36___    /2*pi\     36___    /2*pi\
x24 = \/ 6 *cos|----| + I*\/ 6 *sin|----|
               \ 9  /              \ 9  /

$$x_{24} = \sqrt[36]{6} \cos{\left (\frac{2 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{2 \pi}{9} \right )}$$

        36___    /5*pi\     36___    /5*pi\
x25 = - \/ 6 *cos|----| - I*\/ 6 *sin|----|
                 \ 18 /              \ 18 /

$$x_{25} = - \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$

        36___    /5*pi\     36___    /5*pi\
x26 = - \/ 6 *cos|----| + I*\/ 6 *sin|----|
                 \ 18 /              \ 18 /

$$x_{26} = - \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$

      36___    /5*pi\     36___    /5*pi\
x27 = \/ 6 *cos|----| - I*\/ 6 *sin|----|
               \ 18 /              \ 18 /

$$x_{27} = \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$

      36___    /5*pi\     36___    /5*pi\
x28 = \/ 6 *cos|----| + I*\/ 6 *sin|----|
               \ 18 /              \ 18 /

$$x_{28} = \sqrt[36]{6} \cos{\left (\frac{5 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{5 \pi}{18} \right )}$$

        36___    /7*pi\     36___    /7*pi\
x29 = - \/ 6 *cos|----| - I*\/ 6 *sin|----|
                 \ 18 /              \ 18 /

$$x_{29} = - \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$

        36___    /7*pi\     36___    /7*pi\
x30 = - \/ 6 *cos|----| + I*\/ 6 *sin|----|
                 \ 18 /              \ 18 /

$$x_{30} = - \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$

      36___    /7*pi\     36___    /7*pi\
x31 = \/ 6 *cos|----| - I*\/ 6 *sin|----|
               \ 18 /              \ 18 /

$$x_{31} = \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} - \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$

      36___    /7*pi\     36___    /7*pi\
x32 = \/ 6 *cos|----| + I*\/ 6 *sin|----|
               \ 18 /              \ 18 /

$$x_{32} = \sqrt[36]{6} \cos{\left (\frac{7 \pi}{18} \right )} + \sqrt[36]{6} i \sin{\left (\frac{7 \pi}{18} \right )}$$

        36___    /4*pi\     36___    /4*pi\
x33 = - \/ 6 *cos|----| - I*\/ 6 *sin|----|
                 \ 9  /              \ 9  /

$$x_{33} = - \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$

        36___    /4*pi\     36___    /4*pi\
x34 = - \/ 6 *cos|----| + I*\/ 6 *sin|----|
                 \ 9  /              \ 9  /

$$x_{34} = - \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$

      36___    /4*pi\     36___    /4*pi\
x35 = \/ 6 *cos|----| - I*\/ 6 *sin|----|
               \ 9  /              \ 9  /

$$x_{35} = \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} - \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$

      36___    /4*pi\     36___    /4*pi\
x36 = \/ 6 *cos|----| + I*\/ 6 *sin|----|
               \ 9  /              \ 9  /

$$x_{36} = \sqrt[36]{6} \cos{\left (\frac{4 \pi}{9} \right )} + \sqrt[36]{6} i \sin{\left (\frac{4 \pi}{9} \right )}$$

Численный ответ

x1 = -1.03506296944 - 0.182509528244*i

x2 = -0.359473596826 - 0.98764559017*i

x3 = -0.182509528244 - 1.03506296944*i

x4 = 0.98764559017 + 0.359473596826*i

x5 = -0.67558937261 - 0.805136061926*i

x6 = 1.03506296944 + 0.182509528244*i

x7 = -0.91021909942 + 0.525515242071*i

x8 = 0.805136061926 - 0.67558937261*i

x9 = -0.359473596826 + 0.98764559017*i

x10 = 0.67558937261 - 0.805136061926*i

x11 = -0.67558937261 + 0.805136061926*i

x12 = -0.805136061926 - 0.67558937261*i

x13 = -1.05103048414*i

x14 = 0.182509528244 - 1.03506296944*i

x15 = -0.805136061926 + 0.67558937261*i

x16 = 0.805136061926 + 0.67558937261*i

x17 = 1.03506296944 - 0.182509528244*i

x18 = -0.91021909942 - 0.525515242071*i

x19 = 0.525515242071 + 0.91021909942*i

x20 = 0.359473596826 - 0.98764559017*i

x21 = -0.182509528244 + 1.03506296944*i

x22 = 1.05103048414*i

x23 = -1.03506296944 + 0.182509528244*i

x24 = -1.05103048414000

x25 = 0.359473596826 + 0.98764559017*i

x26 = 0.91021909942 - 0.525515242071*i

x27 = 0.525515242071 - 0.91021909942*i

x28 = 0.182509528244 + 1.03506296944*i

x29 = 0.98764559017 - 0.359473596826*i

x30 = 0.91021909942 + 0.525515242071*i

x31 = -0.98764559017 + 0.359473596826*i

x32 = -0.525515242071 + 0.91021909942*i

x33 = 1.05103048414000

x34 = 0.67558937261 + 0.805136061926*i

x35 = -0.98764559017 - 0.359473596826*i

x36 = -0.525515242071 - 0.91021909942*i

График