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cos^3x-cos^2x-cosx=1/3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
   3         2                  
cos (x) - cos (x) - cos(x) = 1/3
(cos⁡3(x)−cos⁡2(x))−cos⁡(x)=13\left(\cos^{3}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - \cos{\left(x \right)} = \frac{1}{3}
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Gráfica
0-80-60-40-2020406080-1001001-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
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   /                          //
x1=−re⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2)))+2π−iim⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2)))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   /                          //
x2=−re⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3))+2π−iim⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3))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   /                          //
x3=re⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2)))+iim⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2)))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   /                          //
x4=re⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3))+iim⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3))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   //
x5=2π−iim⁡(acos⁡(13+2233+2233))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   //
x6=re⁡(acos⁡(13+2233+2233))+iim⁡(acos⁡(13+2233+2233))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   /                          //
((2π−iim⁡(acos⁡(13+2233+2233)))+((re⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3))+iim⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3)))+(((−re⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2)))+2π−iim⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2))))+(−re⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3))+2π−iim⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3))))+(re⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2)))+iim⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2)))))))+(re⁡(acos⁡(13+2233+2233))+iim⁡(acos⁡(13+2233+2233)))\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   //
re⁡(acos⁡(13+2233+2233))+6π\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   /                          ///
(−re⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2)))+2π−iim⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2))))(−re⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3))+2π−iim⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3)))(re⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2)))+iim⁡(acos⁡(13+223(−12−3i2)3+2233(−12−3i2))))(re⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3))+iim⁡(acos⁡(13+2233(−12+3i2)+223(−12+3i2)3)))(2π−iim⁡(acos⁡(13+2233+2233)))(re⁡(acos⁡(13+2233+2233))+iim⁡(acos⁡(13+2233+2233)))\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      ///
(2π−iim⁡(acos⁡(13+2233+2233)))(re⁡(acos⁡(13+2233+2233))+iim⁡(acos⁡(13+2233+2233)))(re⁡(acos⁡(−233−2236+13−233i3+2233i6))+iim⁡(acos⁡(−233−2236+13−233i3+2233i6)))(re⁡(acos⁡(−233−2236+13−2233i6+233i3))+iim⁡(acos⁡(−233−2236+13−2233i6+233i3)))(−2π+re⁡(acos⁡(−233−2236+13−233i3+2233i6))+iim⁡(acos⁡(−233−2236+13−233i3+2233i6)))(−2π+re⁡(acos⁡(−233−2236+13−2233i6+233i3))+iim⁡(acos⁡(−233−2236+13−2233i6+233i3)))\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
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