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- La ecuación:
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Ecuación 2x^2-8=0
-
Ecuación x^4+x^3+x^2+x+1=0
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Ecuación 2^x=-4
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Ecuación 15/x=3
- Expresar {x} en función de y en la ecuación:
- 14*x+17*y=19
- -14*x+19*y=-3
- -12*x-11*y=19
- 13*x-11*y=16
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Expresiones idénticas
- 4sin^ dos ((π/ tres)-x)+4cos^ dos ((π/ tres)+x)= cinco
- 4 seno de al cuadrado ((π dividir por 3) menos x) más 4 coseno de al cuadrado ((π dividir por 3) más x) es igual a 5
- 4 seno de en el grado dos ((π dividir por tres) menos x) más 4 coseno de en el grado dos ((π dividir por tres) más x) es igual a cinco
- 4sin2((π/3)-x)+4cos2((π/3)+x)=5
- 4sin2π/3-x+4cos2π/3+x=5
- 4sin²((π/3)-x)+4cos²((π/3)+x)=5
- 4sin en el grado 2((π/3)-x)+4cos en el grado 2((π/3)+x)=5
- 4sin^2π/3-x+4cos^2π/3+x=5
- 4sin^2((π dividir por 3)-x)+4cos^2((π dividir por 3)+x)=5
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Expresiones semejantes
- 4sin^2((π/3)+x)+4cos^2((π/3)+x)=5
- 4sin^2((π/3)-x)+4cos^2((π/3)-x)=5
- 4sin^2((π/3)-x)-4cos^2((π/3)+x)=5
4sin^2((π/3)-x)+4cos^2((π/3)+x)=5 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2/pi \ 2/pi \
4*sin |-- - x| + 4*cos |-- + x| = 5
\3 / \3 /
$$4 \sin^{2}{\left(- x + \frac{\pi}{3} \right)} + 4 \cos^{2}{\left(x + \frac{\pi}{3} \right)} = 5$$
Suma y producto de raíces
[src]
suma
/ / / ____\\\ / / / ____\\\ / / ____\ \
| | |\/ 11 ||| / _________________________________________\ | | |\/ 11 ||| / _________________________________________\ | |\/ 11 | |
| |atan|------||| | / / / ____\\ / / ____\\ | | |atan|------||| | / / / ____\\ / / ____\\ | | -I*atan|------| | / ____\
| | \ 11 /|| | / | |\/ 11 || | |\/ 11 || | | | \ 11 /|| | / | |\/ 11 || | |\/ 11 || | | \ 11 / | |\/ 11 |
|cos|------------|| | / |atan|------|| |atan|------|| | |cos|------------|| | / |atan|------|| |atan|------|| | | ----------------| atan|------|
| \ 2 /| | / 2| \ 11 /| 2| \ 11 /| | | \ 2 /| | / 2| \ 11 /| 2| \ 11 /| | | 2 | \ 11 /
pi - atan|-----------------| - I*log| / cos |------------| + sin |------------| | + - atan|-----------------| - I*log| / cos |------------| + sin |------------| | - I*log\-e / - ------------
| / / ____\\| \\/ \ 2 / \ 2 / / | / / ____\\| \\/ \ 2 / \ 2 / / 2
| | |\/ 11 ||| | | |\/ 11 |||
| |atan|------||| | |atan|------|||
| | \ 11 /|| | | \ 11 /||
|sin|------------|| |sin|------------||
\ \ 2 // \ \ 2 //
$$- \frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} + \left(\left(\left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)}\right) + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} + \pi\right)\right) - i \log{\left(- e^{- \frac{i \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2}} \right)}\right)$$
=
/ / / ____\\\ / / ____\ \
| | |\/ 11 ||| | |\/ 11 | | / _________________________________________\
| |atan|------||| / ____\ | -I*atan|------| | | / / / ____\\ / / ____\\ |
| | \ 11 /|| |\/ 11 | | \ 11 / | | / | |\/ 11 || | |\/ 11 || |
|cos|------------|| atan|------| | ----------------| | / |atan|------|| |atan|------|| |
| \ 2 /| \ 11 / | 2 | | / 2| \ 11 /| 2| \ 11 /| |
pi - 2*atan|-----------------| - ------------ - I*log\-e / - 2*I*log| / cos |------------| + sin |------------| |
| / / ____\\| 2 \\/ \ 2 / \ 2 / /
| | |\/ 11 |||
| |atan|------|||
| | \ 11 /||
|sin|------------||
\ \ 2 //
$$- 2 \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} - \frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} - 2 i \log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} - i \log{\left(- e^{- \frac{i \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2}} \right)} + \pi$$
producto
/ / / / ____\\\ \ / / / / ____\\\ \ / / / ____\ \\ | | | |\/ 11 ||| / _________________________________________\| | | | |\/ 11 ||| / _________________________________________\| | | |\/ 11 | || | | |atan|------||| | / / / ____\\ / / ____\\ || | | |atan|------||| | / / / ____\\ / / ____\\ || | | -I*atan|------| || / ____\ | | | \ 11 /|| | / | |\/ 11 || | |\/ 11 || || | | | \ 11 /|| | / | |\/ 11 || | |\/ 11 || || | | \ 11 / || |\/ 11 | | |cos|------------|| | / |atan|------|| |atan|------|| || | |cos|------------|| | / |atan|------|| |atan|------|| || | | ----------------|| -atan|------| | | \ 2 /| | / 2| \ 11 /| 2| \ 11 /| || | | \ 2 /| | / 2| \ 11 /| 2| \ 11 /| || | | 2 || \ 11 / |pi - atan|-----------------| - I*log| / cos |------------| + sin |------------| ||*|- atan|-----------------| - I*log| / cos |------------| + sin |------------| ||*\-I*log\-e //*-------------- | | / / ____\\| \\/ \ 2 / \ 2 / /| | | / / ____\\| \\/ \ 2 / \ 2 / /| 2 | | | |\/ 11 ||| | | | | |\/ 11 ||| | | | |atan|------||| | | | |atan|------||| | | | | \ 11 /|| | | | | \ 11 /|| | | |sin|------------|| | | |sin|------------|| | \ \ \ 2 // / \ \ \ 2 // /
$$- i \log{\left(- e^{- \frac{i \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2}} \right)} \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} + \pi\right) \left(- \frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2}\right)$$
=
/ / ____\ \
| |\/ 11 | |
| -I*atan|------| |
| \ 11 / |
/ / ____\\ / / ____\\ / ____\ | ----------------|
| |\/ 11 || | |\/ 11 || |\/ 11 | | 2 |
-I*|pi - atan|------||*|pi + atan|------||*atan|------|*log\-e /
\ \ 11 // \ \ 11 // \ 11 /
--------------------------------------------------------------------------------
8
$$- \frac{i \left(\pi - \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}\right) \left(\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)} + \pi\right) \log{\left(- e^{- \frac{i \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2}} \right)} \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{8}$$
-i*(pi - atan(sqrt(11)/11))*(pi + atan(sqrt(11)/11))*atan(sqrt(11)/11)*log(-exp(-i*atan(sqrt(11)/11)/2))/8
Respuesta rápida
[src]
/ / / ____\\\
| | |\/ 11 ||| / _________________________________________\
| |atan|------||| | / / / ____\\ / / ____\\ |
| | \ 11 /|| | / | |\/ 11 || | |\/ 11 || |
|cos|------------|| | / |atan|------|| |atan|------|| |
| \ 2 /| | / 2| \ 11 /| 2| \ 11 /| |
x1 = pi - atan|-----------------| - I*log| / cos |------------| + sin |------------| |
| / / ____\\| \\/ \ 2 / \ 2 / /
| | |\/ 11 |||
| |atan|------|||
| | \ 11 /||
|sin|------------||
\ \ 2 //
$$x_{1} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} + \pi$$
/ / / ____\\\
| | |\/ 11 ||| / _________________________________________\
| |atan|------||| | / / / ____\\ / / ____\\ |
| | \ 11 /|| | / | |\/ 11 || | |\/ 11 || |
|cos|------------|| | / |atan|------|| |atan|------|| |
| \ 2 /| | / 2| \ 11 /| 2| \ 11 /| |
x2 = - atan|-----------------| - I*log| / cos |------------| + sin |------------| |
| / / ____\\| \\/ \ 2 / \ 2 / /
| | |\/ 11 |||
| |atan|------|||
| | \ 11 /||
|sin|------------||
\ \ 2 //
$$x_{2} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}}{\sin{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2} \right)}} \right)}$$
/ / ____\ \
| |\/ 11 | |
| -I*atan|------| |
| \ 11 / |
| ----------------|
| 2 |
x3 = -I*log\-e /
$$x_{3} = - i \log{\left(- e^{- \frac{i \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2}} \right)}$$
/ ____\
|\/ 11 |
-atan|------|
\ 11 /
x4 = --------------
2
$$x_{4} = - \frac{\operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{2}$$
x4 = -atan(sqrt(11)/11)/2
Respuesta numérica
[src]
x1 = -0.146421385864288
x2 = 102.248182627533
x3 = -3.28801403945408
x4 = 2.99517126772551
x5 = -4.5659675945204
x6 = 1.71721771265918
x7 = -1.42437494093061
x8 = 4.85881036624898
x8 = 4.85881036624898