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(a-2)*x^2-2*(a+3)*x+4a=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 (a - 2)*x - 2*(a + 3)*x + 4*a = 0
$$4 a + \left(x^{2} \left(a - 2\right) - x 2 \left(a + 3\right)\right) = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$4 a + \left(x^{2} \left(a - 2\right) - x 2 \left(a + 3\right)\right) = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} - 2 a x + 4 a - 2 x^{2} - 6 x = 0$$
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
$$b = - 2 a - 6$$
$$c = 4 a$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{2 a + \sqrt{- 4 a \left(4 a - 8\right) + \left(- 2 a - 6\right)^{2}} + 6}{2 a - 4}$$
$$x_{2} = \frac{2 a - \sqrt{- 4 a \left(4 a - 8\right) + \left(- 2 a - 6\right)^{2}} + 6}{2 a - 4}$$
$$4 a + \left(x^{2} \left(a - 2\right) - x 2 \left(a + 3\right)\right) = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} - 2 a x + 4 a - 2 x^{2} - 6 x = 0$$
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
False
$$b = - 2 a - 6$$
$$c = 4 a$$
, entonces
D = b^2 - 4 * a * c =
(-6 - 2*a)^2 - 4 * (-2 + a) * (4*a) = (-6 - 2*a)^2 - 4*a*(-8 + 4*a)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{2 a + \sqrt{- 4 a \left(4 a - 8\right) + \left(- 2 a - 6\right)^{2}} + 6}{2 a - 4}$$
$$x_{2} = \frac{2 a - \sqrt{- 4 a \left(4 a - 8\right) + \left(- 2 a - 6\right)^{2}} + 6}{2 a - 4}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$4 a + \left(x^{2} \left(a - 2\right) - x 2 \left(a + 3\right)\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{4 a + x^{2} \left(a - 2\right) - x \left(2 a + 6\right)}{a - 2} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{- 2 a - 6}{a - 2}$$
$$q = \frac{c}{a}$$
$$q = \frac{4 a}{a - 2}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{- 2 a - 6}{a - 2}$$
$$x_{1} x_{2} = \frac{4 a}{a - 2}$$
$$4 a + \left(x^{2} \left(a - 2\right) - x 2 \left(a + 3\right)\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{4 a + x^{2} \left(a - 2\right) - x \left(2 a + 6\right)}{a - 2} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{- 2 a - 6}{a - 2}$$
$$q = \frac{c}{a}$$
$$q = \frac{4 a}{a - 2}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{- 2 a - 6}{a - 2}$$
$$x_{1} x_{2} = \frac{4 a}{a - 2}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$4 a + x^{2} \left(a - 2\right) - x \left(2 a + 6\right) = 0$$
Коэффициент при x равен
$$a - 2$$
entonces son posibles los casos para a :
$$a < 2$$
$$a = 2$$
Consideremos todos los casos con detalles:
Con
$$a < 2$$
la ecuación será
$$- x^{2} - 8 x + 4 = 0$$
su solución
$$x = -4 + 2 \sqrt{5}$$
$$x = - 2 \sqrt{5} - 4$$
Con
$$a = 2$$
la ecuación será
$$8 - 10 x = 0$$
su solución
$$x = \frac{4}{5}$$
$$4 a + x^{2} \left(a - 2\right) - x \left(2 a + 6\right) = 0$$
Коэффициент при x равен
$$a - 2$$
entonces son posibles los casos para a :
$$a < 2$$
$$a = 2$$
Consideremos todos los casos con detalles:
Con
$$a < 2$$
la ecuación será
$$- x^{2} - 8 x + 4 = 0$$
su solución
$$x = -4 + 2 \sqrt{5}$$
$$x = - 2 \sqrt{5} - 4$$
Con
$$a = 2$$
la ecuación será
$$8 - 10 x = 0$$
su solución
$$x = \frac{4}{5}$$
Gráfica
Suma y producto de raíces
[src]
suma
/ / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ / _____________________________________________________________________ \ / _____________________________________________________________________ \ / / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ / _____________________________________________________________________ \ / _____________________________________________________________________ \ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | |4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | |4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | |(-2 + re(a))*|- \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)| |3 - \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)|*im(a)| (-2 + re(a))*|3 - \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)| |- \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)|*im(a) |(-2 + re(a))*|\/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)| |3 + \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)|*im(a)| (-2 + re(a))*|3 + \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)| |\/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)|*im(a) | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / I*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------- + I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------ | 2 2 2 2 | 2 2 2 2 | 2 2 2 2 | 2 2 2 2 \ (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) / (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) \ (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) / (-2 + re(a)) + im (a) (-2 + re(a)) + im (a)
$$\left(\frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(\frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 2\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - 2\right) \left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \left(\frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(\frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 2\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - 2\right) \left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right)$$
=
/ / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ / / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ / _____________________________________________________________________ \ / _____________________________________________________________________ \ / _____________________________________________________________________ \ / _____________________________________________________________________ \ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | |4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | |4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | |(-2 + re(a))*|\/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)| |3 + \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)|*im(a)| |(-2 + re(a))*|- \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)| |3 - \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)|*im(a)| (-2 + re(a))*|3 + \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)| (-2 + re(a))*|3 - \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)| |\/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)|*im(a) |- \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)|*im(a) | \ \ 2 / / \ \ 2 / / | | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / \ \ 2 / / \ \ 2 / / I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------ + -------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 2 2 2 2 | | 2 2 2 2 | 2 2 2 2 2 2 2 2 \ (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) / \ (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) / (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) (-2 + re(a)) + im (a)
$$\frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(\frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 2\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + i \left(\frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 2\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - 2\right) \left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(a\right)} - 2\right) \left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
producto
/ / / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ / / / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | | |4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | |4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | |(-2 + re(a))*|- \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)| |3 - \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)|*im(a)| (-2 + re(a))*|3 - \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)| |- \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)|*im(a)| | |(-2 + re(a))*|\/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)| |3 + \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)|*im(a)| (-2 + re(a))*|3 + \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)| |\/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)|*im(a)| | | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / | | | \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / / | |I*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------| | | 2 2 2 2 | 2 2 2 2 | | | 2 2 2 2 | 2 2 2 2 | \ \ (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) / (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) / \ \ (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) / (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) /
$$\left(\frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(\frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 2\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - 2\right) \left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) \left(\frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(\frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 2\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - 2\right) \left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right)$$
=
2 2
-8*re(a) + 4*im (a) + 4*re (a) - 8*I*im(a)
------------------------------------------
2 2
4 + im (a) + re (a) - 4*re(a)
$$\frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 8 \operatorname{re}{\left(a\right)} + 4 \left(\operatorname{im}{\left(a\right)}\right)^{2} - 8 i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} - 4 \operatorname{re}{\left(a\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4}$$
(-8*re(a) + 4*im(a)^2 + 4*re(a)^2 - 8*i*im(a))/(4 + im(a)^2 + re(a)^2 - 4*re(a))
Respuesta rápida
[src]
/ / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ / _____________________________________________________________________ \ / _____________________________________________________________________ \
| | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ |
| | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| |
|(-2 + re(a))*|- \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)| |3 - \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)|*im(a)| (-2 + re(a))*|3 - \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)| |- \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)|*im(a)
| \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / /
x1 = I*|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) / (-2 + re(a)) + im (a) (-2 + re(a)) + im (a)
$$x_{1} = \frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(\frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 2\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - 2\right) \left(- \sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
/ / _____________________________________________________________________ \ / _____________________________________________________________________ \ \ / _____________________________________________________________________ \ / _____________________________________________________________________ \
| | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ |
| |4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | | | 4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| | |4 / 2 / 2 2 \ |atan2\14*im(a) - 6*im(a)*re(a), 9 - 3*re (a) + 3*im (a) + 14*re(a)/| |
|(-2 + re(a))*|\/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)| |3 + \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)|*im(a)| (-2 + re(a))*|3 + \/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *cos|-------------------------------------------------------------------| + re(a)| |\/ (14*im(a) - 6*im(a)*re(a)) + \9 - 3*re (a) + 3*im (a) + 14*re(a)/ *sin|-------------------------------------------------------------------| + im(a)|*im(a)
| \ \ 2 / / \ \ 2 / / | \ \ 2 / / \ \ 2 / /
x2 = I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ (-2 + re(a)) + im (a) (-2 + re(a)) + im (a) / (-2 + re(a)) + im (a) (-2 + re(a)) + im (a)
$$x_{2} = \frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + i \left(\frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \left(\operatorname{re}{\left(a\right)} - 2\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{\left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(a\right)} - 2\right) \left(\sqrt[4]{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)}\right)^{2} + \left(- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 6 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 14 \operatorname{im}{\left(a\right)},- 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} + 14 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} + 9 \right)}}{2} \right)} + \operatorname{re}{\left(a\right)} + 3\right)}{\left(\operatorname{re}{\left(a\right)} - 2\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x2 = (((-6*re(a)*im(a) + 14*im(a))^2 + (-3*re(a)^2 + 14*re(a) + 3*im(a)^2 + 9)^2)^(1/4)*sin(atan2(-6*re(a)*im(a) + 14*im(a, -3*re(a)^2 + 14*re(a) + 3*im(a)^2 + 9)/2) + im(a))*im(a)/((re(a) - 2)^2 + im(a)^2) + i*((((-6*re(a)*im(a) + 14*im(a))^2 + (-3*re(a)^2 + 14*re(a) + 3*im(a)^2 + 9)^2)^(1/4)*sin(atan2(-6*re(a)*im(a) + 14*im(a), -3*re(a)^2 + 14*re(a) + 3*im(a)^2 + 9)/2) + im(a))*(re(a) - 2)/((re(a) - 2)^2 + im(a)^2) - (((-6*re(a)*im(a) + 14*im(a))^2 + (-3*re(a)^2 + 14*re(a) + 3*im(a)^2 + 9)^2)^(1/4)*cos(atan2(-6*re(a)*im(a) + 14*im(a), -3*re(a)^2 + 14*re(a) + 3*im(a)^2 + 9)/2) + re(a) + 3)*im(a)/((re(a) - 2)^2 + im(a)^2)) + (re(a) - 2)*(((-6*re(a)*im(a) + 14*im(a))^2 + (-3*re(a)^2 + 14*re(a) + 3*im(a)^2 + 9)^2)^(1/4)*cos(atan2(-6*re(a)*im(a) + 14*im(a), -3*re(a)^2 + 14*re(a) + 3*im(a)^2 + 9)/2) + re(a) + 3)/((re(a) - 2)^2 + im(a)^2))