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La ecuación:
Ecuación (x-2)^2+(x-3)^2=2x^2
Ecuación √(x^2-1)=2*x
Ecuación (x-2)^2=(x-9)^2
Ecuación x^2=35
Expresar {x} en función de y en la ecuación:
-9*x-15*y=-4
-13*x+7*y=11
-7*x-7*y=-14
16*x+7*y=8
Expresiones idénticas
(cuatro x^ cuatro -(√ dos / dos)x^ dos + uno)(4x^4+(√ dos / dos)x^ dos + uno)= cero
(4x en el grado 4 menos (√2 dividir por 2)x al cuadrado más 1)(4x en el grado 4 más (√2 dividir por 2)x al cuadrado más 1) es igual a 0
(cuatro x en el grado cuatro menos (√ dos dividir por dos)x en el grado dos más uno)(4x en el grado 4 más (√ dos dividir por dos)x en el grado dos más uno) es igual a cero
(4x4-(√2/2)x2+1)(4x4+(√2/2)x2+1)=0
4x4-√2/2x2+14x4+√2/2x2+1=0
(4x⁴-(√2/2)x²+1)(4x⁴+(√2/2)x²+1)=0
(4x en el grado 4-(√2/2)x en el grado 2+1)(4x en el grado 4+(√2/2)x en el grado 2+1)=0
4x^4-√2/2x^2+14x^4+√2/2x^2+1=0
(4x^4-(√2/2)x^2+1)(4x^4+(√2/2)x^2+1)=O
(4x^4-(√2 dividir por 2)x^2+1)(4x^4+(√2 dividir por 2)x^2+1)=0
Expresiones semejantes
(4x^4-(√2/2)x^2+1)(4x^4+(√2/2)x^2-1)=0
(4x^4-(√2/2)x^2-1)(4x^4+(√2/2)x^2+1)=0
(4x^4+(√2/2)x^2+1)(4x^4+(√2/2)x^2+1)=0
(4x^4-(√2/2)x^2+1)(4x^4-(√2/2)x^2+1)=0

(4x^4-(√2/2)x^2+1)(4x^4+(√2/2)x^2+1)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

/         ___       \ /         ___       \    
|   4   \/ 2   2    | |   4   \/ 2   2    |    
|4*x  - -----*x  + 1|*|4*x  + -----*x  + 1| = 0
\         2         / \         2         /

\left(\left(4 x^{4} - x^{2} \frac{\sqrt{2}}{2}\right) + 1\right) \left(\left(4 x^{4} + x^{2} \frac{\sqrt{2}}{2}\right) + 1\right) = 0

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

                                                             /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\
                                                             |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||
                                                             |    |   |atan|------||||                                                           |    |   |atan|------||||
                                                             |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||
                                                             |    |cos|------------|||                                                           |    |cos|------------|||
                                                             |    |   \     2      /||                                                           |    |   \     2      /||
                _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||
               /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||
              /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||
             /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||
            /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||
           /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||
          /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|
x1 = - 4 /       ------------------ + ------------------ *sin|-----------------------| - I*4 /       ------------------ + ------------------ *cos|-----------------------|
       \/                4                    4              \           2           /     \/                4                    4              \           2           /

x_{1} = - \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}

                                                             /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\
                                                             |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||
                                                             |    |   |atan|------||||                                                           |    |   |atan|------||||
                                                             |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||
                                                             |    |cos|------------|||                                                           |    |cos|------------|||
                                                             |    |   \     2      /||                                                           |    |   \     2      /||
                _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||
               /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||
              /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||
             /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||
            /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||
           /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||
          /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|
x2 = - 4 /       ------------------ + ------------------ *sin|-----------------------| + I*4 /       ------------------ + ------------------ *cos|-----------------------|
       \/                4                    4              \           2           /     \/                4                    4              \           2           /

x_{2} = - \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}

                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\
                                                           |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||
                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||
                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||
                                                           |    |cos|------------|||                                                           |    |cos|------------|||
                                                           |    |   \     2      /||                                                           |    |   \     2      /||
              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||
             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||
            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||
           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||
          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||
         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||
        /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|
x3 = 4 /       ------------------ + ------------------ *sin|-----------------------| - I*4 /       ------------------ + ------------------ *cos|-----------------------|
     \/                4                    4              \           2           /     \/                4                    4              \           2           /

x_{3} = \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}

                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\
                                                           |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||
                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||
                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||
                                                           |    |cos|------------|||                                                           |    |cos|------------|||
                                                           |    |   \     2      /||                                                           |    |   \     2      /||
              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||
             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||
            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||
           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||
          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||
         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||
        /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|
x4 = 4 /       ------------------ + ------------------ *sin|-----------------------| + I*4 /       ------------------ + ------------------ *cos|-----------------------|
     \/                4                    4              \           2           /     \/                4                    4              \           2           /

x_{4} = \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}

                                                             /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\
                                                             |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||
                                                             |    |   |atan|------||||                                                           |    |   |atan|------||||
                                                             |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||
                                                             |    |cos|------------|||                                                           |    |cos|------------|||
                                                             |    |   \     2      /||                                                           |    |   \     2      /||
                _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||
               /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||
              /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||
             /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||
            /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||
           /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||
          /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|
x5 = - 4 /       ------------------ + ------------------ *cos|-----------------------| - I*4 /       ------------------ + ------------------ *sin|-----------------------|
       \/                4                    4              \           2           /     \/                4                    4              \           2           /

x_{5} = - \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}

                                                             /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\
                                                             |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||
                                                             |    |   |atan|------||||                                                           |    |   |atan|------||||
                                                             |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||
                                                             |    |cos|------------|||                                                           |    |cos|------------|||
                                                             |    |   \     2      /||                                                           |    |   \     2      /||
                _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||
               /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||
              /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||
             /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||
            /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||
           /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||
          /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|
x6 = - 4 /       ------------------ + ------------------ *cos|-----------------------| + I*4 /       ------------------ + ------------------ *sin|-----------------------|
       \/                4                    4              \           2           /     \/                4                    4              \           2           /

x_{6} = - \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}

                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\
                                                           |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||
                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||
                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||
                                                           |    |cos|------------|||                                                           |    |cos|------------|||
                                                           |    |   \     2      /||                                                           |    |   \     2      /||
              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||
             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||
            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||
           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||
          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||
         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||
        /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|
x7 = 4 /       ------------------ + ------------------ *cos|-----------------------| - I*4 /       ------------------ + ------------------ *sin|-----------------------|
     \/                4                    4              \           2           /     \/                4                    4              \           2           /

x_{7} = \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}

                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\
                                                           |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||
                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||
                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||
                                                           |    |cos|------------|||                                                           |    |cos|------------|||
                                                           |    |   \     2      /||                                                           |    |   \     2      /||
              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||
             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||
            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||
           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||
          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||
         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||
        /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|
x8 = 4 /       ------------------ + ------------------ *cos|-----------------------| + I*4 /       ------------------ + ------------------ *sin|-----------------------|
     \/                4                    4              \           2           /     \/                4                    4              \           2           /

x_{8} = \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}

x8 = (sin(atan(sqrt(31)/15)/2)^2/4 + cos(atan(sqrt(31)/15)/2)^2/4)^(1/4)*cos(atan(cos(atan(sqrt(31)/15)/2)/sin(atan(sqrt(31)/15)/2))/2) + i*(sin(atan(sqrt(31)/15)/2)^2/4 + cos(atan(sqrt(31)/15)/2)^2/4)^(1/4)*sin(atan(cos(atan(sqrt(31)/15)/2)/sin(atan(sqrt(31)/15)/2))/2)

Suma y producto de raíces [src]

suma

                                                        /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                         /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                         /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                         /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\                                                         /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\
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                                                        |    |   |atan|------||||                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||                                                         |    |   |atan|------||||                                                           |    |   |atan|------||||                                                         |    |   |atan|------||||                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||                                                           |    |   |atan|------||||                                                         |    |   |atan|------||||                                                           |    |   |atan|------||||                                                         |    |   |atan|------||||                                                           |    |   |atan|------||||
                                                        |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                         |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                         |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                         |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||                                                         |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||
                                                        |    |cos|------------|||                                                           |    |cos|------------|||                                                           |    |cos|------------|||                                                           |    |cos|------------|||                                                         |    |cos|------------|||                                                           |    |cos|------------|||                                                         |    |cos|------------|||                                                           |    |cos|------------|||                                                           |    |cos|------------|||                                                           |    |cos|------------|||                                                           |    |cos|------------|||                                                           |    |cos|------------|||                                                         |    |cos|------------|||                                                           |    |cos|------------|||                                                         |    |cos|------------|||                                                           |    |cos|------------|||
                                                        |    |   \     2      /||                                                           |    |   \     2      /||                                                           |    |   \     2      /||                                                           |    |   \     2      /||                                                         |    |   \     2      /||                                                           |    |   \     2      /||                                                         |    |   \     2      /||                                                           |    |   \     2      /||                                                           |    |   \     2      /||                                                           |    |   \     2      /||                                                           |    |   \     2      /||                                                           |    |   \     2      /||                                                         |    |   \     2      /||                                                           |    |   \     2      /||                                                         |    |   \     2      /||                                                           |    |   \     2      /||
           _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||            _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||            _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||            _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||            _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||
          /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||           /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||           /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||           /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||           /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||
         /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||          /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||          /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||          /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||          /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||
        /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||         /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||         /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||         /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||         /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||
       /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||        /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||        /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||        /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||        /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||
      /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||       /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||       /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||       /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||       /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||
     /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|      /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|      /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|        /          \     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 /       ------------------ + ------------------ *sin|-----------------------| - I*4 /       ------------------ + ------------------ *cos|-----------------------| + - 4 /       ------------------ + ------------------ *sin|-----------------------| + I*4 /       ------------------ + ------------------ *cos|-----------------------| + 4 /       ------------------ + ------------------ *sin|-----------------------| - I*4 /       ------------------ + ------------------ *cos|-----------------------| + 4 /       ------------------ + ------------------ *sin|-----------------------| + I*4 /       ------------------ + ------------------ *cos|-----------------------| + - 4 /       ------------------ + ------------------ *cos|-----------------------| - I*4 /       ------------------ + ------------------ *sin|-----------------------| + - 4 /       ------------------ + ------------------ *cos|-----------------------| + I*4 /       ------------------ + ------------------ *sin|-----------------------| + 4 /       ------------------ + ------------------ *cos|-----------------------| - I*4 /       ------------------ + ------------------ *sin|-----------------------| + 4 /       ------------------ + ------------------ *cos|-----------------------| + I*4 /       ------------------ + ------------------ *sin|-----------------------|
  \/                4                    4              \           2           /     \/                4                    4              \           2           /     \/                4                    4              \           2           /     \/                4                    4              \           2           /   \/                4                    4              \           2           /     \/                4                    4              \           2           /   \/                4                    4              \           2           /     \/                4                    4              \           2           /     \/                4                    4              \           2           /     \/                4                    4              \           2           /     \/                4                    4              \           2           /     \/                4                    4              \           2           /   \/                4                    4              \           2           /     \/                4                    4              \           2           /   \/                4                    4              \           2           /     \/                4                    4              \           2           /

\left(\left(\sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) + \left(\left(\left(- \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) + \left(\left(\left(\sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) + \left(\left(- \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) + \left(- \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right)\right)\right) + \left(\sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right)\right)\right) + \left(- \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right)\right)\right) + \left(\sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right)

0

producto

/                                                        /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\\ /                                                        /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\\ /                                                      /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\\ /                                                      /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\\ /                                                        /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\\ /                                                        /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\\ /                                                      /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\\ /                                                      /    /   /    /  ____\\\\                                                           /    /   /    /  ____\\\\\
|                                                        |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||| |                                                        |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||| |                                                      |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||| |                                                      |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||| |                                                        |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||| |                                                        |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||| |                                                      |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 ||||| |                                                      |    |   |    |\/ 31 ||||                                                           |    |   |    |\/ 31 |||||
|                                                        |    |   |atan|------||||                                                           |    |   |atan|------||||| |                                                        |    |   |atan|------||||                                                           |    |   |atan|------||||| |                                                      |    |   |atan|------||||                                                           |    |   |atan|------||||| |                                                      |    |   |atan|------||||                                                           |    |   |atan|------||||| |                                                        |    |   |atan|------||||                                                           |    |   |atan|------||||| |                                                        |    |   |atan|------||||                                                           |    |   |atan|------||||| |                                                      |    |   |atan|------||||                                                           |    |   |atan|------||||| |                                                      |    |   |atan|------||||                                                           |    |   |atan|------|||||
|                                                        |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||| |                                                        |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||| |                                                      |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||| |                                                      |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||| |                                                        |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||| |                                                        |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||| |                                                      |    |   |    \  15  /|||                                                           |    |   |    \  15  /|||| |                                                      |    |   |    \  15  /|||                                                           |    |   |    \  15  /||||
|                                                        |    |cos|------------|||                                                           |    |cos|------------|||| |                                                        |    |cos|------------|||                                                           |    |cos|------------|||| |                                                      |    |cos|------------|||                                                           |    |cos|------------|||| |                                                      |    |cos|------------|||                                                           |    |cos|------------|||| |                                                        |    |cos|------------|||                                                           |    |cos|------------|||| |                                                        |    |cos|------------|||                                                           |    |cos|------------|||| |                                                      |    |cos|------------|||                                                           |    |cos|------------|||| |                                                      |    |cos|------------|||                                                           |    |cos|------------||||
|                                                        |    |   \     2      /||                                                           |    |   \     2      /||| |                                                        |    |   \     2      /||                                                           |    |   \     2      /||| |                                                      |    |   \     2      /||                                                           |    |   \     2      /||| |                                                      |    |   \     2      /||                                                           |    |   \     2      /||| |                                                        |    |   \     2      /||                                                           |    |   \     2      /||| |                                                        |    |   \     2      /||                                                           |    |   \     2      /||| |                                                      |    |   \     2      /||                                                           |    |   \     2      /||| |                                                      |    |   \     2      /||                                                           |    |   \     2      /|||
|           _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||| |           _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||| |         _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||| |         _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||| |           _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||| |           _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||| |         _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------||| |         _________________________________________    |atan|-----------------||              _________________________________________    |atan|-----------------|||
|          /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||| |          /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||| |        /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||| |        /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||| |          /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||| |          /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||| |        /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||| |        /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\||             /     /    /  ____\\       /    /  ____\\     |    |   /    /  ____\\|||
|         /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||| |         /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||| |       /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||| |       /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||| |         /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||| |         /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||| |       /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||| |       /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 ||||            /      |    |\/ 31 ||       |    |\/ 31 ||     |    |   |    |\/ 31 |||||
|        /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||| |        /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||| |      /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||| |      /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||| |        /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||| |        /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||| |      /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------||||| |      /       |atan|------||       |atan|------||     |    |   |atan|------||||           /       |atan|------||       |atan|------||     |    |   |atan|------|||||
|       /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||| |       /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||| |     /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||| |     /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||| |       /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||| |       /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||| |     /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||| |     /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /|||          /       2|    \  15  /|      2|    \  15  /|     |    |   |    \  15  /||||
|      /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||| |      /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||| |    /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||| |    /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||| |      /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||| |      /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||| |    /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------|||| |    /     cos |------------|   sin |------------|     |    |sin|------------|||         /     cos |------------|   sin |------------|     |    |sin|------------||||
|     /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|| |     /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|| |   /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|| |   /          \     2      /       \     2      /     |    \   \     2      //|        /          \     2      /       \     2      /     |    \   \     2      //|| |     /          \     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 /       ------------------ + ------------------ *sin|-----------------------| - I*4 /       ------------------ + ------------------ *cos|-----------------------||*|- 4 /       ------------------ + ------------------ *sin|-----------------------| + I*4 /       ------------------ + ------------------ *cos|-----------------------||*|4 /       ------------------ + ------------------ *sin|-----------------------| - I*4 /       ------------------ + ------------------ *cos|-----------------------||*|4 /       ------------------ + ------------------ *sin|-----------------------| + I*4 /       ------------------ + ------------------ *cos|-----------------------||*|- 4 /       ------------------ + ------------------ *cos|-----------------------| - I*4 /       ------------------ + ------------------ *sin|-----------------------||*|- 4 /       ------------------ + ------------------ *cos|-----------------------| + I*4 /       ------------------ + ------------------ *sin|-----------------------||*|4 /       ------------------ + ------------------ *cos|-----------------------| - I*4 /       ------------------ + ------------------ *sin|-----------------------||*|4 /       ------------------ + ------------------ *cos|-----------------------| + I*4 /       ------------------ + ------------------ *sin|-----------------------||
\  \/                4                    4              \           2           /     \/                4                    4              \           2           // \  \/                4                    4              \           2           /     \/                4                    4              \           2           // \\/                4                    4              \           2           /     \/                4                    4              \           2           // \\/                4                    4              \           2           /     \/                4                    4              \           2           // \  \/                4                    4              \           2           /     \/                4                    4              \           2           // \  \/                4                    4              \           2           /     \/                4                    4              \           2           // \\/                4                    4              \           2           /     \/                4                    4              \           2           // \\/                4                    4              \           2           /     \/                4                    4              \           2           //

\left(- \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) \left(- \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) \left(\sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) \left(\sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) \left(- \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) \left(- \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) \left(\sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} - i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right) \left(\sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \cos{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)} + i \sqrt[4]{\frac{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4} + \frac{\cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{4}} \sin{\left(\frac{\operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{2} \right)}} \right)}}{2} \right)}\right)

        /    /  ____\\       /    /  ____\\       /    /  ____\\         /    /  ____\\         /    /  ____\\
        |    |\/ 31 ||       |    |\/ 31 ||       |    |\/ 31 ||         |    |\/ 31 ||         |    |\/ 31 ||
        |atan|------||       |atan|------||       |atan|------||         |atan|------||         |atan|------||
       8|    \  15  /|      6|    \  15  /|      6|    \  15  /|        4|    \  15  /|        8|    \  15  /|
  3*cos |------------|   sin |------------|   cos |------------|   3*sin |------------|   3*sin |------------|
        \     4      /       \     4      /       \     4      /         \     4      /         \     4      /
- -------------------- - ------------------ + ------------------ + -------------------- + --------------------
           16                    2                    4                     8                      16

- \frac{3 \cos^{8}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{4} \right)}}{16} - \frac{\sin^{6}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{4} \right)}}{2} + \frac{3 \sin^{8}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{4} \right)}}{16} + \frac{3 \sin^{4}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{4} \right)}}{8} + \frac{\cos^{6}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{31}}{15} \right)}}{4} \right)}}{4}

-3*cos(atan(sqrt(31)/15)/4)^8/16 - sin(atan(sqrt(31)/15)/4)^6/2 + cos(atan(sqrt(31)/15)/4)^6/4 + 3*sin(atan(sqrt(31)/15)/4)^4/8 + 3*sin(atan(sqrt(31)/15)/4)^8/16

Respuesta numérica [src]

x1 = -0.453658270260601 - 0.542396694149364*i

x2 = -0.542396694149364 + 0.453658270260601*i

x3 = 0.453658270260601 + 0.542396694149364*i

x4 = -0.453658270260601 + 0.542396694149364*i

x5 = 0.542396694149364 - 0.453658270260601*i

x6 = 0.453658270260601 - 0.542396694149364*i

x7 = -0.542396694149364 - 0.453658270260601*i

x8 = 0.542396694149364 + 0.453658270260601*i

x8 = 0.542396694149364 + 0.453658270260601*i

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(4x^4-(√2/2)x^2+1)(4x^4+(√2/2)x^2+1)=0 la ecuación

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