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Expresiones semejantes
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Expresiones con funciones
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xy-y-x^3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Teorema de Cardano-Vieta
reescribamos la ecuación
$$- x^{3} + \left(x y - y\right) = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - x y + y = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - y$$
$$v = \frac{d}{a}$$
$$v = y$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - y$$
$$x_{1} x_{2} x_{3} = y$$
$$- x^{3} + \left(x y - y\right) = 0$$
de
$$a x^{3} + b x^{2} + c x + d = 0$$
como ecuación cúbica reducida
$$x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0$$
$$x^{3} - x y + y = 0$$
$$p x^{2} + q x + v + x^{3} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - y$$
$$v = \frac{d}{a}$$
$$v = y$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 0$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - y$$
$$x_{1} x_{2} x_{3} = y$$
Gráfica
Respuesta rápida
[src]
/ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\\ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\
| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||
| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|||| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|||
| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|||
| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /||| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /||
| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
| / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /|| / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /|
| 6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ y \ | / y \ \/ \ 2 2 / \ 2 2 / \ 3 /| \/ \ 2 2 / \ 2 2 / \ 3 /
x1 = - re|-------------------------------------| + I*|- im|-------------------------------------| - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| _______________________________| | | _______________________________| 3 | 3
| / ___________________ | | | / ___________________ | |
| / / 3 2 | | | / / 3 2 | |
| / \/ - 108*y + 729*y 27*y | | | / \/ - 108*y + 729*y 27*y | |
|3 / ---------------------- + ---- | | |3 / ---------------------- + ---- | |
\\/ 2 2 / \ \\/ 2 2 / /
$$x_{1} = i \left(- \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{3} - \operatorname{im}{\left(\frac{y}{\sqrt[3]{\frac{27 y}{2} + \frac{\sqrt{- 108 y^{3} + 729 y^{2}}}{2}}}\right)}\right) - \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{3} - \operatorname{re}{\left(\frac{y}{\sqrt[3]{\frac{27 y}{2} + \frac{\sqrt{- 108 y^{3} + 729 y^{2}}}{2}}}\right)}$$
/ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\\ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\
| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\|| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\|| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||
| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/||| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|||| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/||| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|||
| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|||
| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /||| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /||
| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
| / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /| ___ / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /|| / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /| ___ / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /|
| 6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ y \ | / y \ \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /| \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /
x2 = - re|-----------------------------------------------------| + I*|- im|-----------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| _______________________________| | | _______________________________| 6 6 | 6 6
| / ___________________ | | | / ___________________ | |
|/ ___\ / / 3 2 | | |/ ___\ / / 3 2 | |
|| 1 I*\/ 3 | / \/ - 108*y + 729*y 27*y | | || 1 I*\/ 3 | / \/ - 108*y + 729*y 27*y | |
||- - - -------|*3 / ---------------------- + ---- | | ||- - - -------|*3 / ---------------------- + ---- | |
\\ 2 2 / \/ 2 2 / \ \\ 2 2 / \/ 2 2 / /
$$x_{2} = - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{6} + \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{6} + i \left(\frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{6} + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{6} - \operatorname{im}{\left(\frac{y}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 y}{2} + \frac{\sqrt{- 108 y^{3} + 729 y^{2}}}{2}}}\right)}\right) - \operatorname{re}{\left(\frac{y}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 y}{2} + \frac{\sqrt{- 108 y^{3} + 729 y^{2}}}{2}}}\right)}$$
/ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\\ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\ _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ \\
| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\|| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\|| / 2 2 | | / 2 2 / / 3 2 2 3 2 2 \\ / 2 2 / / 3 2 2 3 2 2 \\||
| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/||| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|||| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/||| / / ____________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________ \ | | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/| 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|||
| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------||| / | / 2 2 / / 3 2 2 3 2 2 \\| | / 2 2 / / 3 2 2 3 2 2 \\| | | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------| \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|||
| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /||| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | 4 / / 3 2 \ / 2 3 2 2 \ |atan2\108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y), - 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /||
| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *sin|------------------------------------------------------------------------------------------------------------------|| | \/ \108*im (y) - 324*re (y)*im(y) + 1458*im(y)*re(y)/ + \- 729*im (y) - 108*re (y) + 729*re (y) + 324*im (y)*re(y)/ *cos|------------------------------------------------------------------------------------------------------------------|| |atan2|-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
| / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /| ___ / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /|| / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /| ___ / |27*im(y) \ 2 /| |27*re(y) \ 2 /| | \ 2 2 2 2 /|
| 6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + |-------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ y \ | / y \ \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /| \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /
x3 = - re|-----------------------------------------------------| + I*|- im|-----------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| _______________________________| | | _______________________________| 6 6 | 6 6
| / ___________________ | | | / ___________________ | |
|/ ___\ / / 3 2 | | |/ ___\ / / 3 2 | |
|| 1 I*\/ 3 | / \/ - 108*y + 729*y 27*y | | || 1 I*\/ 3 | / \/ - 108*y + 729*y 27*y | |
||- - + -------|*3 / ---------------------- + ---- | | ||- - + -------|*3 / ---------------------- + ---- | |
\\ 2 2 / \/ 2 2 / \ \\ 2 2 / \/ 2 2 / /
$$x_{3} = \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{6} + \frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{6} + i \left(\frac{\sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{6} - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2}\right)^{2} + \left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{im}{\left(y\right)}}{2},\frac{\sqrt[4]{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3}\right)^{2} + \left(- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 324 \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 1458 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 108 \left(\operatorname{im}{\left(y\right)}\right)^{3},- 108 \left(\operatorname{re}{\left(y\right)}\right)^{3} + 729 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 324 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 729 \left(\operatorname{im}{\left(y\right)}\right)^{2} \right)}}{2} \right)}}{2} + \frac{27 \operatorname{re}{\left(y\right)}}{2} \right)}}{3} \right)}}{6} - \operatorname{im}{\left(\frac{y}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 y}{2} + \frac{\sqrt{- 108 y^{3} + 729 y^{2}}}{2}}}\right)}\right) - \operatorname{re}{\left(\frac{y}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27 y}{2} + \frac{\sqrt{- 108 y^{3} + 729 y^{2}}}{2}}}\right)}$$
x3 = sqrt(3)*((((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*sin(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*im(y)/2)^2 + (((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*cos(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*re(y)/2)^2)^(1/6)*sin(atan2(((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*sin(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*im(y)/2, ((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*cos(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*re(y)/2)/3)/6 + ((((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*sin(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*im(y)/2)^2 + (((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*cos(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*re(y)/2)^2)^(1/6)*cos(atan2(((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*sin(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*im(y)/2, ((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*cos(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*re(y)/2)/3)/6 + i*(((((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*sin(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*im(y)/2)^2 + (((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*cos(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*re(y)/2)^2)^(1/6)*sin(atan2(((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*sin(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*im(y)/2, ((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*cos(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*re(y)/2)/3)/6 - sqrt(3)*((((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*sin(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*im(y)/2)^2 + (((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*cos(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*re(y)/2)^2)^(1/6)*cos(atan2(((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*sin(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*im(y)/2, ((-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3)^2 + (-108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)^2)^(1/4)*cos(atan2(-324*re(y)^2*im(y) + 1458*re(y)*im(y) + 108*im(y)^3, -108*re(y)^3 + 729*re(y)^2 + 324*re(y)*im(y)^2 - 729*im(y)^2)/2)/2 + 27*re(y)/2)/3)/6 - im(y/((-1/2 + sqrt(3)*i/2)*(27*y/2 + sqrt(-108*y^3 + 729*y^2)/2)^(1/3)))) - re(y/((-1/2 + sqrt(3)*i/2)*(27*y/2 + sqrt(-108*y^3 + 729*y^2)/2)^(1/3))))