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- La ecuación:
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Ecuación 8*x=2
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Ecuación 3^x=81
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Ecuación 5x+15=x-1
-
Ecuación x^2=12
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -17*x+2*y=9
-
Expresiones idénticas
- 2sin²x+√ tres *cosx=√ seis *cosx(-π\ cuatro)
- 2 seno de ²x más √3 multiplicar por coseno de x es igual a √6 multiplicar por coseno de x( menos π\4)
- 2 seno de ²x más √ tres multiplicar por coseno de x es igual a √ seis multiplicar por coseno de x( menos π\ cuatro)
- 2sin²x+√3cosx=√6cosx(-π\4)
- 2sin²x+√3cosx=√6cosx-π\4
-
Expresiones semejantes
- 2sin²x-√3*cosx=√6*cosx(-π\4)
- 2sin²x+√3*cosx=√6*cosx(π\4)
-
Expresiones con funciones
- cosx
- cosx=p/2
- cosx=10
- cosx+sinx=1/(2)^1/2
- cosx-0,5x+1=0
- cosx+Csinx=0
- cosx
- cosx=p/2
- cosx=10
- cosx+sinx=1/(2)^1/2
- cosx-0,5x+1=0
- cosx+Csinx=0
2sin²x+√3*cosx=√6*cosx(-π\4) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 ___ ___ -pi
2*sin (x) + \/ 3 *cos(x) = \/ 6 *cos(x)*----
4
$$2 \sin^{2}{\left(x \right)} + \sqrt{3} \cos{\left(x \right)} = \frac{\left(-1\right) \pi}{4} \sqrt{6} \cos{\left(x \right)}$$
Solución detallada
Tenemos la ecuación
$$2 \sin^{2}{\left(x \right)} + \sqrt{3} \cos{\left(x \right)} = \frac{\left(-1\right) \pi}{4} \sqrt{6} \cos{\left(x \right)}$$
cambiamos
$$2 \sin^{2}{\left(x \right)} + \sqrt{3} \cos{\left(x \right)} + \frac{\sqrt{6} \pi \cos{\left(x \right)}}{4} = 0$$
$$- \frac{\left(-1\right) \pi}{4} \sqrt{6} \cos{\left(x \right)} - 2 \cos^{2}{\left(x \right)} + \sqrt{3} \cos{\left(x \right)} + 2 = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -2$$
$$b = \sqrt{3} + \frac{\sqrt{6} \pi}{4}$$
$$c = 2$$
, entonces
Como D > 0 la ecuación tiene dos raíces.
o
$$w_{1} = - \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16}$$
$$w_{2} = \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4}$$
hacemos cambio inverso
$$\cos{\left(x \right)} = w$$
Tenemos la ecuación
$$\cos{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
O
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} \right)}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(w_{2} \right)}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} \right)}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} \right)}$$
$$x_{3} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{3} = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} \right)}$$
$$x_{3} = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} \right)}$$
$$x_{4} = \pi n + \operatorname{acos}{\left(w_{2} \right)} - \pi$$
$$x_{4} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} \right)}$$
$$x_{4} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} \right)}$$
$$2 \sin^{2}{\left(x \right)} + \sqrt{3} \cos{\left(x \right)} = \frac{\left(-1\right) \pi}{4} \sqrt{6} \cos{\left(x \right)}$$
cambiamos
$$2 \sin^{2}{\left(x \right)} + \sqrt{3} \cos{\left(x \right)} + \frac{\sqrt{6} \pi \cos{\left(x \right)}}{4} = 0$$
$$- \frac{\left(-1\right) \pi}{4} \sqrt{6} \cos{\left(x \right)} - 2 \cos^{2}{\left(x \right)} + \sqrt{3} \cos{\left(x \right)} + 2 = 0$$
Sustituimos
$$w = \cos{\left(x \right)}$$
Es la ecuación de la forma
a*w^2 + b*w + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = -2$$
$$b = \sqrt{3} + \frac{\sqrt{6} \pi}{4}$$
$$c = 2$$
, entonces
D = b^2 - 4 * a * c =
(sqrt(3) + pi*sqrt(6)/4)^2 - 4 * (-2) * (2) = 16 + (sqrt(3) + pi*sqrt(6)/4)^2
Como D > 0 la ecuación tiene dos raíces.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b - sqrt(D)) / (2*a)
o
$$w_{1} = - \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16}$$
$$w_{2} = \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4}$$
hacemos cambio inverso
$$\cos{\left(x \right)} = w$$
Tenemos la ecuación
$$\cos{\left(x \right)} = w$$
es la ecuación trigonométrica más simple
Esta ecuación se reorganiza en
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
O
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, donde n es cualquier número entero
sustituimos w:
$$x_{1} = \pi n + \operatorname{acos}{\left(w_{1} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} \right)}$$
$$x_{1} = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} \right)}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(w_{2} \right)}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} \right)}$$
$$x_{2} = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} \right)}$$
$$x_{3} = \pi n + \operatorname{acos}{\left(w_{1} \right)} - \pi$$
$$x_{3} = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} \right)}$$
$$x_{3} = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} + \frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} \right)}$$
$$x_{4} = \pi n + \operatorname{acos}{\left(w_{2} \right)} - \pi$$
$$x_{4} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} \right)}$$
$$x_{4} = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{4} + \frac{\sqrt{6} \pi}{16} + \frac{\sqrt{\left(\sqrt{3} + \frac{\sqrt{6} \pi}{4}\right)^{2} + 16}}{4} \right)}$$
Respuesta rápida
[src]
/ ___________________________________________________________________________________________________\
| / ___________________________ ___________________________ |
| 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ |
|3 *\/ -128 + 16*pi - 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 + \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 |
x1 = -2*atan|------------------------------------------------------------------------------------------------------------|
| __________ ______________ |
| / 2 / ___ |
\ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 /
$$x_{1} = - 2 \operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}$$
/ ___________________________________________________________________________________________________\
| / ___________________________ ___________________________ |
| 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ |
|3 *\/ -128 + 16*pi - 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 + \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 |
x2 = 2*atan|------------------------------------------------------------------------------------------------------------|
| __________ ______________ |
| / 2 / ___ |
\ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 /
$$x_{2} = 2 \operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}$$
/ / ___________________________________________________________________________________________________\\
| | / ___________________________ ___________________________ ||
| | 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ ||
| |3 *\/ -128 + 16*pi + 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 - \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 ||
x3 = -2*I*im|atan|------------------------------------------------------------------------------------------------------------||
| | __________ ______________ ||
| | / 2 / ___ ||
\ \ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 //
$$x_{3} = - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}\right)}$$
/ / ___________________________________________________________________________________________________\\
| | / ___________________________ ___________________________ ||
| | 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ ||
| |3 *\/ -128 + 16*pi + 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 - \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 ||
x4 = 2*I*im|atan|------------------------------------------------------------------------------------------------------------||
| | __________ ______________ ||
| | / 2 / ___ ||
\ \ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 //
$$x_{4} = 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}\right)}$$
x4 = 2*i*im(atan(3^(3/4)*sqrt(-sqrt(2)*pi^2*sqrt(3*pi^2 + 12*sqrt(2)*pi + 152) - 128 + 16*pi^2 + 8*sqrt(2)*sqrt(3*pi^2 + 12*sqrt(2)*pi + 152))/(3*sqrt(-8 + pi^2)*sqrt(4 + sqrt(2)*pi))))
Suma y producto de raíces
[src]
suma
/ ___________________________________________________________________________________________________\ / ___________________________________________________________________________________________________\ / / ___________________________________________________________________________________________________\\ / / ___________________________________________________________________________________________________\\
| / ___________________________ ___________________________ | | / ___________________________ ___________________________ | | | / ___________________________ ___________________________ || | | / ___________________________ ___________________________ ||
| 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ | | 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ | | | 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ || | | 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ ||
|3 *\/ -128 + 16*pi - 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 + \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 | |3 *\/ -128 + 16*pi - 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 + \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 | | |3 *\/ -128 + 16*pi + 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 - \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 || | |3 *\/ -128 + 16*pi + 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 - \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 ||
- 2*atan|------------------------------------------------------------------------------------------------------------| + 2*atan|------------------------------------------------------------------------------------------------------------| - 2*I*im|atan|------------------------------------------------------------------------------------------------------------|| + 2*I*im|atan|------------------------------------------------------------------------------------------------------------||
| __________ ______________ | | __________ ______________ | | | __________ ______________ || | | __________ ______________ ||
| / 2 / ___ | | / 2 / ___ | | | / 2 / ___ || | | / 2 / ___ ||
\ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 / \ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 / \ \ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 // \ \ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 //
$$\left(\left(- 2 \operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)} + 2 \operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}\right) - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}\right)}\right) + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}\right)}$$
=
0
$$0$$
producto
/ ___________________________________________________________________________________________________\ / ___________________________________________________________________________________________________\ / / ___________________________________________________________________________________________________\\ / / ___________________________________________________________________________________________________\\
| / ___________________________ ___________________________ | | / ___________________________ ___________________________ | | | / ___________________________ ___________________________ || | | / ___________________________ ___________________________ ||
| 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ | | 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ | | | 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ || | | 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ ||
|3 *\/ -128 + 16*pi - 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 + \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 | |3 *\/ -128 + 16*pi - 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 + \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 | | |3 *\/ -128 + 16*pi + 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 - \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 || | |3 *\/ -128 + 16*pi + 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 - \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 ||
-2*atan|------------------------------------------------------------------------------------------------------------|*2*atan|------------------------------------------------------------------------------------------------------------|*-2*I*im|atan|------------------------------------------------------------------------------------------------------------||*2*I*im|atan|------------------------------------------------------------------------------------------------------------||
| __________ ______________ | | __________ ______________ | | | __________ ______________ || | | __________ ______________ ||
| / 2 / ___ | | / 2 / ___ | | | / 2 / ___ || | | / 2 / ___ ||
\ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 / \ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 / \ \ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 // \ \ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 //
$$2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}\right)} - 2 \operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)} 2 \operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}$$
=
/ ___________________________________________________________________________________________________\ / / ___________________________________________________________________________________________________\\
| / ___________________________ ___________________________ | | | / ___________________________ ___________________________ ||
| 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ | | | 3/4 / 2 ___ / 2 ___ ___ 2 / 2 ___ ||
2|3 *\/ -128 + 16*pi - 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 + \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 | 2| |3 *\/ -128 + 16*pi + 8*\/ 2 *\/ 152 + 3*pi + 12*pi*\/ 2 - \/ 2 *pi *\/ 152 + 3*pi + 12*pi*\/ 2 ||
-16*atan |------------------------------------------------------------------------------------------------------------|*im |atan|------------------------------------------------------------------------------------------------------------||
| __________ ______________ | | | __________ ______________ ||
| / 2 / ___ | | | / 2 / ___ ||
\ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 / \ \ 3*\/ -8 + pi *\/ 4 + pi*\/ 2 //
$$- 16 \left(\operatorname{im}{\left(\operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{- \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}\right)}\right)^{2} \operatorname{atan}^{2}{\left(\frac{3^{\frac{3}{4}} \sqrt{- 8 \sqrt{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152} - 128 + 16 \pi^{2} + \sqrt{2} \pi^{2} \sqrt{3 \pi^{2} + 12 \sqrt{2} \pi + 152}}}{3 \sqrt{-8 + \pi^{2}} \sqrt{4 + \sqrt{2} \pi}} \right)}$$
-16*atan(3^(3/4)*sqrt(-128 + 16*pi^2 - 8*sqrt(2)*sqrt(152 + 3*pi^2 + 12*pi*sqrt(2)) + sqrt(2)*pi^2*sqrt(152 + 3*pi^2 + 12*pi*sqrt(2)))/(3*sqrt(-8 + pi^2)*sqrt(4 + pi*sqrt(2))))^2*im(atan(3^(3/4)*sqrt(-128 + 16*pi^2 + 8*sqrt(2)*sqrt(152 + 3*pi^2 + 12*pi*sqrt(2)) - sqrt(2)*pi^2*sqrt(152 + 3*pi^2 + 12*pi*sqrt(2)))/(3*sqrt(-8 + pi^2)*sqrt(4 + pi*sqrt(2)))))^2
Respuesta numérica
[src]
x1 = 54.5214062095155
x2 = 89.991855855615
x3 = 79.6541474382338
x4 = -27.1600027838191
x5 = 48.2382209023359
x6 = 98.5037033597726
x7 = 23.1054796736176
x8 = -4.25592375207882
x9 = 71.1422999340762
x10 = -23.1054796736176
x11 = -39.7263733981783
x12 = -83.7086705484354
x13 = 96.2750411627946
x14 = 20.8768174766395
x15 = -60.8045915166951
x16 = -96.2750411627946
x17 = -33.4431880909987
x18 = 2.02726155510077
x19 = 16.822294366438
x20 = -48.2382209023359
x21 = -52.2927440125375
x22 = -89.991855855615
x23 = -54.5214062095155
x24 = 41.9550355951563
x25 = 58.575929319717
x26 = -77.4254852412558
x27 = -8.31044686228035
x28 = 92.220518052593
x29 = 14.5936321694599
x30 = -92.220518052593
x31 = -10.5391090592584
x32 = -67.0877768238747
x33 = 85.9373327454134
x34 = -58.575929319717
x35 = -79.6541474382338
x36 = 64.8591146268966
x37 = -2.02726155510077
x38 = -35.6718502879768
x39 = -286.99926257516
x40 = 35.6718502879768
x41 = 52.2927440125375
x42 = -71.1422999340762
x43 = -73.3709621310543
x44 = 4.25592375207882
x45 = 60.8045915166951
x46 = 10.5391090592584
x47 = 46.0095587053579
x48 = -98.5037033597726
x49 = 77.4254852412558
x50 = -46.0095587053579
x51 = -29.3886649807972
x52 = 33.4431880909987
x53 = -16.822294366438
x54 = 8.31044686228035
x55 = -64.8591146268966
x56 = 39.7263733981783
x57 = -14.5936321694599
x58 = 83.7086705484354
x59 = -85.9373327454134
x60 = -20.8768174766395
x61 = 29.3886649807972
x62 = -41.9550355951563
x63 = 73.3709621310543
x63 = 73.3709621310543