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Ecuación 1+sin(x)=0
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Ecuación 2*x^2+6*x+9=
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- Derivada de:
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1/3
- Integral de d{x}:
- 1/3
- Límite de la función:
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1/3
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Expresiones idénticas
- cos^ tres x-cos^2x-cosx= uno /3
- coseno de al cubo x menos coseno de al cuadrado x menos coseno de x es igual a 1 dividir por 3
- coseno de en el grado tres x menos coseno de al cuadrado x menos coseno de x es igual a uno dividir por 3
- cos3x-cos2x-cosx=1/3
- cos³x-cos²x-cosx=1/3
- cos en el grado 3x-cos en el grado 2x-cosx=1/3
- cos^3x-cos^2x-cosx=1 dividir por 3
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Expresiones semejantes
- (x²-4)/5-(x²-1)/3=-1
- cos^3x+cos^2x-cosx=1/3
- 2*x^5-1/(3*x^2)+4*x^(1/4)=y
- cos^3x-cos^2x+cosx=1/3
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Expresiones con funciones
- Coseno cos
- cos(pi*x)=1
- cos(x+(pi/6))=1
- cos(x)/3=0
- cos(2*x)+cos(x)=0
- cos(8*pi*x/6)=sqrt(3)/2
- Coseno cos
- cos(pi*x)=1
- cos(x+(pi/6))=1
- cos(x)/3=0
- cos(2*x)+cos(x)=0
- cos(8*pi*x/6)=sqrt(3)/2
- cosx
- cosx=√3/2
- cosx+1,3-lnx=0
- cosx=п/3
- cosx=-1.2
- cosx-lnx=0
cos^3x-cos^2x-cosx=1/3 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 2 cos (x) - cos (x) - cos(x) = 1/3
$$\left(\cos^{3}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - \cos{\left(x \right)} = \frac{1}{3}$$
Respuesta rápida
[src]
/ / / ___\\\ / / / ___\\\
| | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 |||
| | 2/3 2*\/ 2 *|- - - -------||| | | 2/3 2*\/ 2 *|- - - -------|||
| |1 2 \ 2 2 /|| | |1 2 \ 2 2 /||
x1 = - re|acos|- + ----------------- + -----------------------|| + 2*pi - I*im|acos|- + ----------------- + -----------------------||
| |3 / ___\ 3 || | |3 / ___\ 3 ||
| | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | ||
| | 3*|- - - -------| || | | 3*|- - - -------| ||
\ \ \ 2 2 / // \ \ \ 2 2 / //
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)}$$
/ / / ___\\\ / / / ___\\\
| | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 |||
| | 2/3 2*\/ 2 *|- - + -------||| | | 2/3 2*\/ 2 *|- - + -------|||
| |1 2 \ 2 2 /|| | |1 2 \ 2 2 /||
x2 = - re|acos|- + ----------------- + -----------------------|| + 2*pi - I*im|acos|- + ----------------- + -----------------------||
| |3 / ___\ 3 || | |3 / ___\ 3 ||
| | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | ||
| | 3*|- - + -------| || | | 3*|- - + -------| ||
\ \ \ 2 2 / // \ \ \ 2 2 / //
$$x_{2} = - \operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)}$$
/ / / ___\\\ / / / ___\\\
| | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 |||
| | 2/3 2*\/ 2 *|- - - -------||| | | 2/3 2*\/ 2 *|- - - -------|||
| |1 2 \ 2 2 /|| | |1 2 \ 2 2 /||
x3 = I*im|acos|- + ----------------- + -----------------------|| + re|acos|- + ----------------- + -----------------------||
| |3 / ___\ 3 || | |3 / ___\ 3 ||
| | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | ||
| | 3*|- - - -------| || | | 3*|- - - -------| ||
\ \ \ 2 2 / // \ \ \ 2 2 / //
$$x_{3} = \operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)}$$
/ / / ___\\\ / / / ___\\\
| | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 |||
| | 2/3 2*\/ 2 *|- - + -------||| | | 2/3 2*\/ 2 *|- - + -------|||
| |1 2 \ 2 2 /|| | |1 2 \ 2 2 /||
x4 = I*im|acos|- + ----------------- + -----------------------|| + re|acos|- + ----------------- + -----------------------||
| |3 / ___\ 3 || | |3 / ___\ 3 ||
| | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | ||
| | 3*|- - + -------| || | | 3*|- - + -------| ||
\ \ \ 2 2 / // \ \ \ 2 2 / //
$$x_{4} = \operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)}$$
/ / 2/3 3 ___\\
| |1 2 2*\/ 2 ||
x5 = 2*pi - I*im|acos|- + ---- + -------||
\ \3 3 3 //
$$x_{5} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)}$$
/ / 2/3 3 ___\\ / / 2/3 3 ___\\
| |1 2 2*\/ 2 || | |1 2 2*\/ 2 ||
x6 = I*im|acos|- + ---- + -------|| + re|acos|- + ---- + -------||
\ \3 3 3 // \ \3 3 3 //
$$x_{6} = \operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)}$$
x6 = re(acos(1/3 + 2^(2/3)/3 + 2*2^(1/3)/3)) + i*im(acos(1/3 + 2^(2/3)/3 + 2*2^(1/3)/3))
Suma y producto de raíces
[src]
suma
/ / / ___\\\ / / / ___\\\ / / / ___\\\ / / / ___\\\ / / / ___\\\ / / / ___\\\ / / / ___\\\ / / / ___\\\
| | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 |||
| | 2/3 2*\/ 2 *|- - - -------||| | | 2/3 2*\/ 2 *|- - - -------||| | | 2/3 2*\/ 2 *|- - + -------||| | | 2/3 2*\/ 2 *|- - + -------||| | | 2/3 2*\/ 2 *|- - - -------||| | | 2/3 2*\/ 2 *|- - - -------||| | | 2/3 2*\/ 2 *|- - + -------||| | | 2/3 2*\/ 2 *|- - + -------||| / / 2/3 3 ___\\ / / 2/3 3 ___\\ / / 2/3 3 ___\\
| |1 2 \ 2 2 /|| | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /|| | |1 2 2*\/ 2 || | |1 2 2*\/ 2 || | |1 2 2*\/ 2 ||
- re|acos|- + ----------------- + -----------------------|| + 2*pi - I*im|acos|- + ----------------- + -----------------------|| + - re|acos|- + ----------------- + -----------------------|| + 2*pi - I*im|acos|- + ----------------- + -----------------------|| + I*im|acos|- + ----------------- + -----------------------|| + re|acos|- + ----------------- + -----------------------|| + I*im|acos|- + ----------------- + -----------------------|| + re|acos|- + ----------------- + -----------------------|| + 2*pi - I*im|acos|- + ---- + -------|| + I*im|acos|- + ---- + -------|| + re|acos|- + ---- + -------||
| |3 / ___\ 3 || | |3 / ___\ 3 || | |3 / ___\ 3 || | |3 / ___\ 3 || | |3 / ___\ 3 || | |3 / ___\ 3 || | |3 / ___\ 3 || | |3 / ___\ 3 || \ \3 3 3 // \ \3 3 3 // \ \3 3 3 //
| | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | ||
| | 3*|- - - -------| || | | 3*|- - - -------| || | | 3*|- - + -------| || | | 3*|- - + -------| || | | 3*|- - - -------| || | | 3*|- - - -------| || | | 3*|- - + -------| || | | 3*|- - + -------| ||
\ \ \ 2 2 / // \ \ \ 2 2 / // \ \ \ 2 2 / // \ \ \ 2 2 / // \ \ \ 2 2 / // \ \ \ 2 2 / // \ \ \ 2 2 / // \ \ \ 2 2 / //
$$\left(\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)}\right) + \left(\left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)}\right) + \left(\left(\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)}\right)\right)\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)}\right)$$
=
/ / 2/3 3 ___\\
| |1 2 2*\/ 2 ||
6*pi + re|acos|- + ---- + -------||
\ \3 3 3 //
$$\operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)} + 6 \pi$$
producto
/ / / / ___\\\ / / / ___\\\\ / / / / ___\\\ / / / ___\\\\ / / / / ___\\\ / / / ___\\\\ / / / / ___\\\ / / / ___\\\\ | | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 |||| | | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 |||| | | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 |||| | | | 3 ___ | 1 I*\/ 3 ||| | | 3 ___ | 1 I*\/ 3 |||| | | | 2/3 2*\/ 2 *|- - - -------||| | | 2/3 2*\/ 2 *|- - - -------|||| | | | 2/3 2*\/ 2 *|- - + -------||| | | 2/3 2*\/ 2 *|- - + -------|||| | | | 2/3 2*\/ 2 *|- - - -------||| | | 2/3 2*\/ 2 *|- - - -------|||| | | | 2/3 2*\/ 2 *|- - + -------||| | | 2/3 2*\/ 2 *|- - + -------|||| / / / 2/3 3 ___\\\ / / / 2/3 3 ___\\ / / 2/3 3 ___\\\ | | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /||| | | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /||| | | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /||| | | |1 2 \ 2 2 /|| | |1 2 \ 2 2 /||| | | |1 2 2*\/ 2 ||| | | |1 2 2*\/ 2 || | |1 2 2*\/ 2 ||| |- re|acos|- + ----------------- + -----------------------|| + 2*pi - I*im|acos|- + ----------------- + -----------------------|||*|- re|acos|- + ----------------- + -----------------------|| + 2*pi - I*im|acos|- + ----------------- + -----------------------|||*|I*im|acos|- + ----------------- + -----------------------|| + re|acos|- + ----------------- + -----------------------|||*|I*im|acos|- + ----------------- + -----------------------|| + re|acos|- + ----------------- + -----------------------|||*|2*pi - I*im|acos|- + ---- + -------|||*|I*im|acos|- + ---- + -------|| + re|acos|- + ---- + -------||| | | |3 / ___\ 3 || | |3 / ___\ 3 ||| | | |3 / ___\ 3 || | |3 / ___\ 3 ||| | | |3 / ___\ 3 || | |3 / ___\ 3 ||| | | |3 / ___\ 3 || | |3 / ___\ 3 ||| \ \ \3 3 3 /// \ \ \3 3 3 // \ \3 3 3 /// | | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | ||| | | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | ||| | | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | ||| | | | | 1 I*\/ 3 | || | | | 1 I*\/ 3 | ||| | | | 3*|- - - -------| || | | 3*|- - - -------| ||| | | | 3*|- - + -------| || | | 3*|- - + -------| ||| | | | 3*|- - - -------| || | | 3*|- - - -------| ||| | | | 3*|- - + -------| || | | 3*|- - + -------| ||| \ \ \ \ 2 2 / // \ \ \ 2 2 / /// \ \ \ \ 2 2 / // \ \ \ 2 2 / /// \ \ \ \ 2 2 / // \ \ \ 2 2 / /// \ \ \ \ 2 2 / // \ \ \ 2 2 / ///
$$\left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)} + \frac{2 \sqrt[3]{2} \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)}{3} \right)}\right)}\right) \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)}\right)$$
=
/ / / 2/3 3 ___\\\ / / / 2/3 3 ___\\ / / 2/3 3 ___\\\ / / / 3 ___ 2/3 3 ___ ___ 2/3 ___\\ / / 3 ___ 2/3 3 ___ ___ 2/3 ___\\\ / / / 3 ___ 2/3 2/3 ___ 3 ___ ___\\ / / 3 ___ 2/3 2/3 ___ 3 ___ ___\\\ / / / 3 ___ 2/3 3 ___ ___ 2/3 ___\\ / / 3 ___ 2/3 3 ___ ___ 2/3 ___\\\ / / / 3 ___ 2/3 2/3 ___ 3 ___ ___\\ / / 3 ___ 2/3 2/3 ___ 3 ___ ___\\\ | | |1 2 2*\/ 2 ||| | | |1 2 2*\/ 2 || | |1 2 2*\/ 2 ||| | | |1 \/ 2 2 I*\/ 2 *\/ 3 I*2 *\/ 3 || | |1 \/ 2 2 I*\/ 2 *\/ 3 I*2 *\/ 3 ||| | | |1 \/ 2 2 I*2 *\/ 3 I*\/ 2 *\/ 3 || | |1 \/ 2 2 I*2 *\/ 3 I*\/ 2 *\/ 3 ||| | | |1 \/ 2 2 I*\/ 2 *\/ 3 I*2 *\/ 3 || | |1 \/ 2 2 I*\/ 2 *\/ 3 I*2 *\/ 3 ||| | | |1 \/ 2 2 I*2 *\/ 3 I*\/ 2 *\/ 3 || | |1 \/ 2 2 I*2 *\/ 3 I*\/ 2 *\/ 3 ||| |2*pi - I*im|acos|- + ---- + -------|||*|I*im|acos|- + ---- + -------|| + re|acos|- + ---- + -------|||*|I*im|acos|- - ----- - ---- - ------------- + ------------|| + re|acos|- - ----- - ---- - ------------- + ------------|||*|I*im|acos|- - ----- - ---- - ------------ + -------------|| + re|acos|- - ----- - ---- - ------------ + -------------|||*|-2*pi + I*im|acos|- - ----- - ---- - ------------- + ------------|| + re|acos|- - ----- - ---- - ------------- + ------------|||*|-2*pi + I*im|acos|- - ----- - ---- - ------------ + -------------|| + re|acos|- - ----- - ---- - ------------ + -------------||| \ \ \3 3 3 /// \ \ \3 3 3 // \ \3 3 3 /// \ \ \3 3 6 3 6 // \ \3 3 6 3 6 /// \ \ \3 3 6 6 3 // \ \3 3 6 6 3 /// \ \ \3 3 6 3 6 // \ \3 3 6 3 6 /// \ \ \3 3 6 6 3 // \ \3 3 6 6 3 ///
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{1}{3} + \frac{2^{\frac{2}{3}}}{3} + \frac{2 \sqrt[3]{2}}{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{\sqrt[3]{2}}{3} - \frac{2^{\frac{2}{3}}}{6} + \frac{1}{3} - \frac{\sqrt[3]{2} \sqrt{3} i}{3} + \frac{2^{\frac{2}{3}} \sqrt{3} i}{6} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{\sqrt[3]{2}}{3} - \frac{2^{\frac{2}{3}}}{6} + \frac{1}{3} - \frac{\sqrt[3]{2} \sqrt{3} i}{3} + \frac{2^{\frac{2}{3}} \sqrt{3} i}{6} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{\sqrt[3]{2}}{3} - \frac{2^{\frac{2}{3}}}{6} + \frac{1}{3} - \frac{2^{\frac{2}{3}} \sqrt{3} i}{6} + \frac{\sqrt[3]{2} \sqrt{3} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{\sqrt[3]{2}}{3} - \frac{2^{\frac{2}{3}}}{6} + \frac{1}{3} - \frac{2^{\frac{2}{3}} \sqrt{3} i}{6} + \frac{\sqrt[3]{2} \sqrt{3} i}{3} \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{\sqrt[3]{2}}{3} - \frac{2^{\frac{2}{3}}}{6} + \frac{1}{3} - \frac{\sqrt[3]{2} \sqrt{3} i}{3} + \frac{2^{\frac{2}{3}} \sqrt{3} i}{6} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{\sqrt[3]{2}}{3} - \frac{2^{\frac{2}{3}}}{6} + \frac{1}{3} - \frac{\sqrt[3]{2} \sqrt{3} i}{3} + \frac{2^{\frac{2}{3}} \sqrt{3} i}{6} \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{\sqrt[3]{2}}{3} - \frac{2^{\frac{2}{3}}}{6} + \frac{1}{3} - \frac{2^{\frac{2}{3}} \sqrt{3} i}{6} + \frac{\sqrt[3]{2} \sqrt{3} i}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{\sqrt[3]{2}}{3} - \frac{2^{\frac{2}{3}}}{6} + \frac{1}{3} - \frac{2^{\frac{2}{3}} \sqrt{3} i}{6} + \frac{\sqrt[3]{2} \sqrt{3} i}{3} \right)}\right)}\right)$$
(2*pi - i*im(acos(1/3 + 2^(2/3)/3 + 2*2^(1/3)/3)))*(i*im(acos(1/3 + 2^(2/3)/3 + 2*2^(1/3)/3)) + re(acos(1/3 + 2^(2/3)/3 + 2*2^(1/3)/3)))*(i*im(acos(1/3 - 2^(1/3)/3 - 2^(2/3)/6 - i*2^(1/3)*sqrt(3)/3 + i*2^(2/3)*sqrt(3)/6)) + re(acos(1/3 - 2^(1/3)/3 - 2^(2/3)/6 - i*2^(1/3)*sqrt(3)/3 + i*2^(2/3)*sqrt(3)/6)))*(i*im(acos(1/3 - 2^(1/3)/3 - 2^(2/3)/6 - i*2^(2/3)*sqrt(3)/6 + i*2^(1/3)*sqrt(3)/3)) + re(acos(1/3 - 2^(1/3)/3 - 2^(2/3)/6 - i*2^(2/3)*sqrt(3)/6 + i*2^(1/3)*sqrt(3)/3)))*(-2*pi + i*im(acos(1/3 - 2^(1/3)/3 - 2^(2/3)/6 - i*2^(1/3)*sqrt(3)/3 + i*2^(2/3)*sqrt(3)/6)) + re(acos(1/3 - 2^(1/3)/3 - 2^(2/3)/6 - i*2^(1/3)*sqrt(3)/3 + i*2^(2/3)*sqrt(3)/6)))*(-2*pi + i*im(acos(1/3 - 2^(1/3)/3 - 2^(2/3)/6 - i*2^(2/3)*sqrt(3)/6 + i*2^(1/3)*sqrt(3)/3)) + re(acos(1/3 - 2^(1/3)/3 - 2^(2/3)/6 - i*2^(2/3)*sqrt(3)/6 + i*2^(1/3)*sqrt(3)/3)))
Respuesta numérica
[src]
x1 = 6.28318530717959 - 1.12498528475449*i
x2 = 4.36794711519116 - 0.282208350633355*i
x3 = 4.36794711519116 + 0.282208350633355*i
x4 = 1.12498528475449*i
x5 = 1.91523819198842 + 0.282208350633355*i
x6 = 1.91523819198842 - 0.282208350633355*i
x6 = 1.91523819198842 - 0.282208350633355*i