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Ecuación x^4=(x-20)^2
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Ecuación (x+6)^3=25*(x+6)
- Ecuación x+y+2=0
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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
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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 /
$$\left(\left(4 x^{4} - x^{2} \frac{\sqrt{2}}{2}\right) + 1\right) \left(\left(4 x^{4} + x^{2} \frac{\sqrt{2}}{2}\right) + 1\right) = 0$$
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
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suma
/ / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\ / / / / ____\\\\
| | | |\/ 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(\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
$$0$$
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