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Expresiones semejantes
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(a-3)(a+3)x^2-(2a^2+5a-9)x+a+3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 / 2 \ (a - 3)*(a + 3)*x - \2*a + 5*a - 9/*x + a + 3 = 0
$$\left(a + \left(x^{2} \left(a - 3\right) \left(a + 3\right) - x \left(\left(2 a^{2} + 5 a\right) - 9\right)\right)\right) + 3 = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$\left(a + \left(x^{2} \left(a - 3\right) \left(a + 3\right) - x \left(\left(2 a^{2} + 5 a\right) - 9\right)\right)\right) + 3 = 0$$
Obtenemos la ecuación cuadrática
$$a^{2} x^{2} - 2 a^{2} x - 5 a x + a - 9 x^{2} + 9 x + 3 = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = a^{2} - 9$$
$$b = - 2 a^{2} - 5 a + 9$$
$$c = a + 3$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{2 a^{2} + 5 a + \sqrt{- \left(a + 3\right) \left(4 a^{2} - 36\right) + \left(- 2 a^{2} - 5 a + 9\right)^{2}} - 9}{2 a^{2} - 18}$$
$$x_{2} = \frac{2 a^{2} + 5 a - \sqrt{- \left(a + 3\right) \left(4 a^{2} - 36\right) + \left(- 2 a^{2} - 5 a + 9\right)^{2}} - 9}{2 a^{2} - 18}$$
$$\left(a + \left(x^{2} \left(a - 3\right) \left(a + 3\right) - x \left(\left(2 a^{2} + 5 a\right) - 9\right)\right)\right) + 3 = 0$$
Obtenemos la ecuación cuadrática
$$a^{2} x^{2} - 2 a^{2} x - 5 a x + a - 9 x^{2} + 9 x + 3 = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = a^{2} - 9$$
$$b = - 2 a^{2} - 5 a + 9$$
$$c = a + 3$$
, entonces
D = b^2 - 4 * a * c =
(9 - 5*a - 2*a^2)^2 - 4 * (-9 + a^2) * (3 + a) = (9 - 5*a - 2*a^2)^2 - (-36 + 4*a^2)*(3 + a)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{2 a^{2} + 5 a + \sqrt{- \left(a + 3\right) \left(4 a^{2} - 36\right) + \left(- 2 a^{2} - 5 a + 9\right)^{2}} - 9}{2 a^{2} - 18}$$
$$x_{2} = \frac{2 a^{2} + 5 a - \sqrt{- \left(a + 3\right) \left(4 a^{2} - 36\right) + \left(- 2 a^{2} - 5 a + 9\right)^{2}} - 9}{2 a^{2} - 18}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(a + \left(x^{2} \left(a - 3\right) \left(a + 3\right) - x \left(\left(2 a^{2} + 5 a\right) - 9\right)\right)\right) + 3 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a + x^{2} \left(a - 3\right) \left(a + 3\right) - x \left(2 a^{2} + 5 a - 9\right) + 3}{\left(a - 3\right) \left(a + 3\right)} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{- 2 a^{2} - 5 a + 9}{\left(a - 3\right) \left(a + 3\right)}$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{a - 3}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{- 2 a^{2} - 5 a + 9}{\left(a - 3\right) \left(a + 3\right)}$$
$$x_{1} x_{2} = \frac{1}{a - 3}$$
$$\left(a + \left(x^{2} \left(a - 3\right) \left(a + 3\right) - x \left(\left(2 a^{2} + 5 a\right) - 9\right)\right)\right) + 3 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a + x^{2} \left(a - 3\right) \left(a + 3\right) - x \left(2 a^{2} + 5 a - 9\right) + 3}{\left(a - 3\right) \left(a + 3\right)} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{- 2 a^{2} - 5 a + 9}{\left(a - 3\right) \left(a + 3\right)}$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{a - 3}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{- 2 a^{2} - 5 a + 9}{\left(a - 3\right) \left(a + 3\right)}$$
$$x_{1} x_{2} = \frac{1}{a - 3}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a + x^{2} \left(a - 3\right) \left(a + 3\right) - x \left(2 a^{2} + 5 a - 9\right) + 3 = 0$$
Коэффициент при x равен
$$\left(a - 3\right) \left(a + 3\right)$$
entonces son posibles los casos para a :
$$a < -3$$
$$a = -3$$
$$a > -3 \wedge a < 3$$
$$a = 3$$
Consideremos todos los casos con detalles:
Con
$$a < -3$$
la ecuación será
$$7 x^{2} - 3 x - 1 = 0$$
su solución
$$x = \frac{3}{14} - \frac{\sqrt{37}}{14}$$
$$x = \frac{3}{14} + \frac{\sqrt{37}}{14}$$
Con
$$a = -3$$
la ecuación será
$$6 x = 0$$
su solución
$$x = 0$$
Con
$$a > -3 \wedge a < 3$$
la ecuación será
$$- 9 x^{2} + 9 x + 3 = 0$$
su solución
$$x = \frac{1}{2} - \frac{\sqrt{21}}{6}$$
$$x = \frac{1}{2} + \frac{\sqrt{21}}{6}$$
Con
$$a = 3$$
la ecuación será
$$6 - 24 x = 0$$
su solución
$$x = \frac{1}{4}$$
$$a + x^{2} \left(a - 3\right) \left(a + 3\right) - x \left(2 a^{2} + 5 a - 9\right) + 3 = 0$$
Коэффициент при x равен
$$\left(a - 3\right) \left(a + 3\right)$$
entonces son posibles los casos para a :
$$a < -3$$
$$a = -3$$
$$a > -3 \wedge a < 3$$
$$a = 3$$
Consideremos todos los casos con detalles:
Con
$$a < -3$$
la ecuación será
$$7 x^{2} - 3 x - 1 = 0$$
su solución
$$x = \frac{3}{14} - \frac{\sqrt{37}}{14}$$
$$x = \frac{3}{14} + \frac{\sqrt{37}}{14}$$
Con
$$a = -3$$
la ecuación será
$$6 x = 0$$
su solución
$$x = 0$$
Con
$$a > -3 \wedge a < 3$$
la ecuación será
$$- 9 x^{2} + 9 x + 3 = 0$$
su solución
$$x = \frac{1}{2} - \frac{\sqrt{21}}{6}$$
$$x = \frac{1}{2} + \frac{\sqrt{21}}{6}$$
Con
$$a = 3$$
la ecuación será
$$6 - 24 x = 0$$
su solución
$$x = \frac{1}{4}$$
Gráfica
Respuesta rápida
[src]
/ / ____________________________________________________________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________________________________________________________ \ \ / ____________________________________________________________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________________________________________________________ \
| | / 2 2 / / 3 3 3 2 2 4 4 3 2 2 2 2 \\ | | / 2 2 / / 3 3 3 2 2 4 4 3 2 2 2 2 \\| | | / 2 2 / / 3 3 3 2 2 4 4 3 2 2 2 2 \\| | / 2 2 / / 3 3 3 2 2 4 4 3 2 2 2 2 \\ |
|/ 2 2 \ | 4 / / 3 3 3 2 \ / 2 4 4 3 2 2 2 2 \ |atan2\-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a), 189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/| | | 2 2 4 / / 3 3 3 2 \ / 2 4 4 3 2 2 2 2 \ |atan2\-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a), 189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/|| | / 2 2 \ | 2 2 4 / / 3 3 3 2 \ / 2 4 4 3 2 2 2 2 \ |atan2\-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a), 189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/|| | 4 / / 3 3 3 2 \ / 2 4 4 3 2 2 2 2 \ |atan2\-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a), 189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/| |
|\-9 + re (a) - im (a)/*|5*im(a) - \/ \-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a)/ + \189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + 4*im(a)*re(a)| |-9 - 2*im (a) + 2*re (a) + 5*re(a) - \/ \-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a)/ + \189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*im(a)*re(a)| \-9 + re (a) - im (a)/*|-9 - 2*im (a) + 2*re (a) + 5*re(a) - \/ \-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a)/ + \189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| |5*im(a) - \/ \-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a)/ + \189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + 4*im(a)*re(a)|*im(a)*re(a)
| \ \ 2 / / \ \ 2 // | \ \ 2 // \ \ 2 / /
x1 = I*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| / 2 \ 2 | / 2 \ 2
| |/ 2 2 \ 2 2 | / 2 2 \ 2 2 | |/ 2 2 \ 2 2 | / 2 2 \ 2 2
\ 2*\\-9 + re (a) - im (a)/ + 4*im (a)*re (a)/ \-9 + re (a) - im (a)/ + 4*im (a)*re (a) / 2*\\-9 + re (a) - im (a)/ + 4*im (a)*re (a)/ \-9 + re (a) - im (a)/ + 4*im (a)*re (a)
$$x_{1} = i \left(\frac{\left(- \sqrt[4]{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189 \right)}}{2} \right)} + 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 5 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)}{2 \left(\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(- \sqrt[4]{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189 \right)}}{2} \right)} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} - 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(- \sqrt[4]{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189 \right)}}{2} \right)} + 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 5 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right) \left(- \sqrt[4]{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189 \right)}}{2} \right)} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} - 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)}{2 \left(\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}$$
/ / ____________________________________________________________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________________________________________________________ \ \ / ____________________________________________________________________________________________________________________________________________________________________________________________________________________ \ / ____________________________________________________________________________________________________________________________________________________________________________________________________________________ \
| | / 2 2 / / 3 3 3 2 2 4 4 3 2 2 2 2 \\ | | / 2 2 / / 3 3 3 2 2 4 4 3 2 2 2 2 \\| | | / 2 2 / / 3 3 3 2 2 4 4 3 2 2 2 2 \\| | / 2 2 / / 3 3 3 2 2 4 4 3 2 2 2 2 \\ |
|/ 2 2 \ | 4 / / 3 3 3 2 \ / 2 4 4 3 2 2 2 2 \ |atan2\-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a), 189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/| | | 2 2 4 / / 3 3 3 2 \ / 2 4 4 3 2 2 2 2 \ |atan2\-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a), 189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/|| | / 2 2 \ | 2 2 4 / / 3 3 3 2 \ / 2 4 4 3 2 2 2 2 \ |atan2\-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a), 189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/|| | 4 / / 3 3 3 2 \ / 2 4 4 3 2 2 2 2 \ |atan2\-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a), 189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/| |
|\-9 + re (a) - im (a)/*|5*im(a) + \/ \-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a)/ + \189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + 4*im(a)*re(a)| |-9 - 2*im (a) + 2*re (a) + 5*re(a) + \/ \-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a)/ + \189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*im(a)*re(a)| \-9 + re (a) - im (a)/*|-9 - 2*im (a) + 2*re (a) + 5*re(a) + \/ \-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a)/ + \189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/ *cos|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| |5*im(a) + \/ \-54*im(a) - 16*im (a) - 46*im(a)*re(a) - 16*im (a)*re(a) + 16*re (a)*im(a) + 48*re (a)*im(a)/ + \189 - 54*re(a) - 23*re (a) + 4*im (a) + 4*re (a) + 16*re (a) + 23*im (a) - 48*im (a)*re(a) - 24*im (a)*re (a)/ *sin|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + 4*im(a)*re(a)|*im(a)*re(a)
| \ \ 2 / / \ \ 2 // | \ \ 2 // \ \ 2 / /
x2 = I*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| / 2 \ 2 | / 2 \ 2
| |/ 2 2 \ 2 2 | / 2 2 \ 2 2 | |/ 2 2 \ 2 2 | / 2 2 \ 2 2
\ 2*\\-9 + re (a) - im (a)/ + 4*im (a)*re (a)/ \-9 + re (a) - im (a)/ + 4*im (a)*re (a) / 2*\\-9 + re (a) - im (a)/ + 4*im (a)*re (a)/ \-9 + re (a) - im (a)/ + 4*im (a)*re (a)
$$x_{2} = i \left(\frac{\left(\sqrt[4]{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189 \right)}}{2} \right)} + 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 5 \operatorname{im}{\left(a\right)}\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)}{2 \left(\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189 \right)}}{2} \right)} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} - 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\sqrt[4]{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189 \right)}}{2} \right)} + 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 5 \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right) \left(\sqrt[4]{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)}\right)^{2} + \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} + 48 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(a\right)} - 16 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 46 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - 16 \left(\operatorname{im}{\left(a\right)}\right)^{3} - 54 \operatorname{im}{\left(a\right)},4 \left(\operatorname{re}{\left(a\right)}\right)^{4} + 16 \left(\operatorname{re}{\left(a\right)}\right)^{3} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 23 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 48 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 54 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{4} + 23 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 189 \right)}}{2} \right)} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} - 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)}{2 \left(\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(a\right)}\right)^{2} - 9\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}$$
x2 = i*((((16*re(a)^3*im(a) + 48*re(a)^2*im(a) - 16*re(a)*im(a)^3 - 46*re(a)*im(a) - 16*im(a)^3 - 54*im(a))^2 + (4*re(a)^4 + 16*re(a)^3 - 24*re(a)^2*im(a)^2 - 23*re(a)^2 - 48*re(a)*im(a)^2 - 54*re(a) + 4*im(a)^4 + 23*im(a)^2 + 189)^2)^(1/4)*sin(atan2(16*re(a)^3*im(a) + 48*re(a)^2*im(a) - 16*re(a)*im(a)^3 - 46*re(a)*im(a) - 16*im(a)^3 - 54*im(a, 4*re(a)^4 + 16*re(a)^3 - 24*re(a)^2*im(a)^2 - 23*re(a)^2 - 48*re(a)*im(a)^2 - 54*re(a) + 4*im(a)^4 + 23*im(a)^2 + 189)/2) + 4*re(a)*im(a) + 5*im(a))*(re(a)^2 - im(a)^2 - 9)/(2*((re(a)^2 - im(a)^2 - 9)^2 + 4*re(a)^2*im(a)^2)) - (((16*re(a)^3*im(a) + 48*re(a)^2*im(a) - 16*re(a)*im(a)^3 - 46*re(a)*im(a) - 16*im(a)^3 - 54*im(a))^2 + (4*re(a)^4 + 16*re(a)^3 - 24*re(a)^2*im(a)^2 - 23*re(a)^2 - 48*re(a)*im(a)^2 - 54*re(a) + 4*im(a)^4 + 23*im(a)^2 + 189)^2)^(1/4)*cos(atan2(16*re(a)^3*im(a) + 48*re(a)^2*im(a) - 16*re(a)*im(a)^3 - 46*re(a)*im(a) - 16*im(a)^3 - 54*im(a), 4*re(a)^4 + 16*re(a)^3 - 24*re(a)^2*im(a)^2 - 23*re(a)^2 - 48*re(a)*im(a)^2 - 54*re(a) + 4*im(a)^4 + 23*im(a)^2 + 189)/2) + 2*re(a)^2 + 5*re(a) - 2*im(a)^2 - 9)*re(a)*im(a)/((re(a)^2 - im(a)^2 - 9)^2 + 4*re(a)^2*im(a)^2)) + (((16*re(a)^3*im(a) + 48*re(a)^2*im(a) - 16*re(a)*im(a)^3 - 46*re(a)*im(a) - 16*im(a)^3 - 54*im(a))^2 + (4*re(a)^4 + 16*re(a)^3 - 24*re(a)^2*im(a)^2 - 23*re(a)^2 - 48*re(a)*im(a)^2 - 54*re(a) + 4*im(a)^4 + 23*im(a)^2 + 189)^2)^(1/4)*sin(atan2(16*re(a)^3*im(a) + 48*re(a)^2*im(a) - 16*re(a)*im(a)^3 - 46*re(a)*im(a) - 16*im(a)^3 - 54*im(a), 4*re(a)^4 + 16*re(a)^3 - 24*re(a)^2*im(a)^2 - 23*re(a)^2 - 48*re(a)*im(a)^2 - 54*re(a) + 4*im(a)^4 + 23*im(a)^2 + 189)/2) + 4*re(a)*im(a) + 5*im(a))*re(a)*im(a)/((re(a)^2 - im(a)^2 - 9)^2 + 4*re(a)^2*im(a)^2) + (re(a)^2 - im(a)^2 - 9)*(((16*re(a)^3*im(a) + 48*re(a)^2*im(a) - 16*re(a)*im(a)^3 - 46*re(a)*im(a) - 16*im(a)^3 - 54*im(a))^2 + (4*re(a)^4 + 16*re(a)^3 - 24*re(a)^2*im(a)^2 - 23*re(a)^2 - 48*re(a)*im(a)^2 - 54*re(a) + 4*im(a)^4 + 23*im(a)^2 + 189)^2)^(1/4)*cos(atan2(16*re(a)^3*im(a) + 48*re(a)^2*im(a) - 16*re(a)*im(a)^3 - 46*re(a)*im(a) - 16*im(a)^3 - 54*im(a), 4*re(a)^4 + 16*re(a)^3 - 24*re(a)^2*im(a)^2 - 23*re(a)^2 - 48*re(a)*im(a)^2 - 54*re(a) + 4*im(a)^4 + 23*im(a)^2 + 189)/2) + 2*re(a)^2 + 5*re(a) - 2*im(a)^2 - 9)/(2*((re(a)^2 - im(a)^2 - 9)^2 + 4*re(a)^2*im(a)^2)))