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La ecuación:
Ecuación -x/11+x=50/11
Ecuación 12/x=3
Ecuación 6-5(4x-1)=3
Ecuación 13/(x-5)=5/(x-13)
Expresar {x} en función de y en la ecuación:
-1*x+4*y=-10
-11*x-19*y=14
-13*x-19*y=17
8*x+6*y=20
Expresiones idénticas
(cuatro -6sinx)tgx=2sin|x|cosx
(4 menos 6 seno de x)tgx es igual a 2 seno de módulo de x| coseno de x
(cuatro menos 6 seno de x)tgx es igual a 2 seno de módulo de x| coseno de x
4-6sinxtgx=2sin|x|cosx
Expresiones semejantes
(4+6sinx)tgx=2sin|x|cosx
Expresiones con funciones
cosx
cosx-2|cosx|=y
Módulo |
|x|+3=5
||2x-1|-3|=3-|1-2x|
|x|=3,7
|x|=15
|x-2|=1

(4-6sinx)tgx=2sin|x|cosx la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

(4 - 6*sin(x))*tan(x) = 2*sin(|x|)*cos(x)

\left(4 - 6 \sin{\left(x \right)}\right) \tan{\left(x \right)} = 2 \sin{\left(\left|{x}\right| \right)} \cos{\left(x \right)}

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

x1 = 0

x_{1} = 0

x2 = pi

x_{2} = \pi

           /                         ______________\
           |  /      ___\     ___   /          ___ |
           |I*\3 - \/ 5 /   \/ 2 *\/  -5 + 3*\/ 5  |
x3 = -I*log|------------- - -----------------------|
           \      2                    2           /

x_{3} = - i \log{\left(- \frac{\sqrt{2} \sqrt{-5 + 3 \sqrt{5}}}{2} + \frac{i \left(3 - \sqrt{5}\right)}{2} \right)}

           /                         ______________\
           |  /      ___\     ___   /          ___ |
           |I*\3 - \/ 5 /   \/ 2 *\/  -5 + 3*\/ 5  |
x4 = -I*log|------------- + -----------------------|
           \      2                    2           /

x_{4} = - i \log{\left(\frac{\sqrt{2} \sqrt{-5 + 3 \sqrt{5}}}{2} + \frac{i \left(3 - \sqrt{5}\right)}{2} \right)}

         //      /      ___________________                 \                                                                        \     //      /      ___________________                 \                                                                        \
         ||      |     /                 2                  |        /     /      ___________________                 \         \    |     ||      |     /                 2                  |        /     /      ___________________                 \         \    |
         ||      |    /      /      ____\       /      ____\|        |     |     /                 2                  |         |    |     ||      |    /      /      ____\       /      ____\|        |     |     /                 2                  |         |    |
         ||      |  \/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |    /      /      ____\       /      ____\|         |    |     ||      |  \/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |    /      /      ____\       /      ____\|         |    |
x5 = I*im|<-I*log|- ----------------------- - --------------|  for I*\- log\- \/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + re|<-I*log|- ----------------------- - --------------|  for I*\- log\- \/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0|
         ||      \             2                    2       /                                                                        |     ||      \             2                    2       /                                                                        |
         ||                                                                                                                          |     ||                                                                                                                          |
         ||                       nan                                                        otherwise                               |     ||                       nan                                                        otherwise                               |
         \\                                                                                                                          /     \\                                                                                                                          /

x_{5} = \operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} - \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) - \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} - \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) - \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //      /    ___________________                 \                                                                      \     //      /    ___________________                 \                                                                      \
         ||      |   /                 2                  |        /     /    ___________________                 \         \    |     ||      |   /                 2                  |        /     /    ___________________                 \         \    |
         ||      |  /      /      ____\       /      ____\|        |     |   /                 2                  |         |    |     ||      |  /      /      ____\       /      ____\|        |     |   /                 2                  |         |    |
         ||      |\/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |  /      /      ____\       /      ____\|         |    |     ||      |\/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |  /      /      ____\       /      ____\|         |    |
x6 = I*im|<-I*log|----------------------- - --------------|  for I*\- log\\/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + re|<-I*log|----------------------- - --------------|  for I*\- log\\/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0|
         ||      \           2                    2       /                                                                      |     ||      \           2                    2       /                                                                      |
         ||                                                                                                                      |     ||                                                                                                                      |
         ||                      nan                                                      otherwise                              |     ||                      nan                                                      otherwise                              |
         \\                                                                                                                      /     \\                                                                                                                      /

x_{6} = \operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} + \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) + \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} + \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) + \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //      /      __________________                \                                                                       \     //      /      __________________                \                                                                       \
         ||      |     /                2                 |        /     /      __________________                \         \     |     ||      |     /                2                 |        /     /      __________________                \         \     |
         ||      |    /      /      ___\       /      ___\|        |     |     /                2                 |         |     |     ||      |    /      /      ___\       /      ___\|        |     |     /                2                 |         |     |
         ||      |  \/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |    /      /      ___\       /      ___\|         |     |     ||      |  \/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |    /      /      ___\       /      ___\|         |     |
x7 = I*im|<-I*log|- ---------------------- + -------------|  for I*\- log\- \/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + re|<-I*log|- ---------------------- + -------------|  for I*\- log\- \/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0|
         ||      \            2                    2      /                                                                       |     ||      \            2                    2      /                                                                       |
         ||                                                                                                                       |     ||                                                                                                                       |
         ||                      nan                                                       otherwise                              |     ||                      nan                                                       otherwise                              |
         \\                                                                                                                       /     \\                                                                                                                       /

x_{7} = \operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

         //      /    __________________                \                                                                     \     //      /    __________________                \                                                                     \
         ||      |   /                2                 |        /     /    __________________                \         \     |     ||      |   /                2                 |        /     /    __________________                \         \     |
         ||      |  /      /      ___\       /      ___\|        |     |   /                2                 |         |     |     ||      |  /      /      ___\       /      ___\|        |     |   /                2                 |         |     |
         ||      |\/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |  /      /      ___\       /      ___\|         |     |     ||      |\/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |  /      /      ___\       /      ___\|         |     |
x8 = I*im|<-I*log|---------------------- + -------------|  for I*\- log\\/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + re|<-I*log|---------------------- + -------------|  for I*\- log\\/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0|
         ||      \          2                    2      /                                                                     |     ||      \          2                    2      /                                                                     |
         ||                                                                                                                   |     ||                                                                                                                   |
         ||                     nan                                                     otherwise                             |     ||                     nan                                                     otherwise                             |
         \\                                                                                                                   /     \\                                                                                                                   /

x_{8} = \operatorname{re}{\left(\begin{cases} - i \log{\left(\frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(\frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}

x8 = re(Piecewise((-i*log(sqrt(4 - (sqrt(5) + 3)^2)/2 + i*(sqrt(5) + 3)/2, i*(log(2) - log(sqrt(4 - (sqrt(5) + 3)^2) + i*(sqrt(5) + 3))) >= 0), (nan, True))) + i*im(Piecewise((-i*log(sqrt(4 - (sqrt(5) + 3)^2)/2 + i*(sqrt(5) + 3)/2), i*(log(2) - log(sqrt(4 - (sqrt(5) + 3)^2) + i*(sqrt(5) + 3))) >= 0), (nan, True))))

Suma y producto de raíces [src]

suma

                                                                                                           //      /      ___________________                 \                                                                        \     //      /      ___________________                 \                                                                        \       //      /    ___________________                 \                                                                      \     //      /    ___________________                 \                                                                      \       //      /      __________________                \                                                                       \     //      /      __________________                \                                                                       \       //      /    __________________                \                                                                     \     //      /    __________________                \                                                                     \
          /                         ______________\        /                         ______________\       ||      |     /                 2                  |        /     /      ___________________                 \         \    |     ||      |     /                 2                  |        /     /      ___________________                 \         \    |       ||      |   /                 2                  |        /     /    ___________________                 \         \    |     ||      |   /                 2                  |        /     /    ___________________                 \         \    |       ||      |     /                2                 |        /     /      __________________                \         \     |     ||      |     /                2                 |        /     /      __________________                \         \     |       ||      |   /                2                 |        /     /    __________________                \         \     |     ||      |   /                2                 |        /     /    __________________                \         \     |
          |  /      ___\     ___   /          ___ |        |  /      ___\     ___   /          ___ |       ||      |    /      /      ____\       /      ____\|        |     |     /                 2                  |         |    |     ||      |    /      /      ____\       /      ____\|        |     |     /                 2                  |         |    |       ||      |  /      /      ____\       /      ____\|        |     |   /                 2                  |         |    |     ||      |  /      /      ____\       /      ____\|        |     |   /                 2                  |         |    |       ||      |    /      /      ___\       /      ___\|        |     |     /                2                 |         |     |     ||      |    /      /      ___\       /      ___\|        |     |     /                2                 |         |     |       ||      |  /      /      ___\       /      ___\|        |     |   /                2                 |         |     |     ||      |  /      /      ___\       /      ___\|        |     |   /                2                 |         |     |
          |I*\3 - \/ 5 /   \/ 2 *\/  -5 + 3*\/ 5  |        |I*\3 - \/ 5 /   \/ 2 *\/  -5 + 3*\/ 5  |       ||      |  \/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |    /      /      ____\       /      ____\|         |    |     ||      |  \/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |    /      /      ____\       /      ____\|         |    |       ||      |\/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |  /      /      ____\       /      ____\|         |    |     ||      |\/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |  /      /      ____\       /      ____\|         |    |       ||      |  \/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |    /      /      ___\       /      ___\|         |     |     ||      |  \/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |    /      /      ___\       /      ___\|         |     |       ||      |\/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |  /      /      ___\       /      ___\|         |     |     ||      |\/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |  /      /      ___\       /      ___\|         |     |
pi - I*log|------------- - -----------------------| - I*log|------------- + -----------------------| + I*im|<-I*log|- ----------------------- - --------------|  for I*\- log\- \/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + re|<-I*log|- ----------------------- - --------------|  for I*\- log\- \/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + I*im|<-I*log|----------------------- - --------------|  for I*\- log\\/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + re|<-I*log|----------------------- - --------------|  for I*\- log\\/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + I*im|<-I*log|- ---------------------- + -------------|  for I*\- log\- \/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + re|<-I*log|- ---------------------- + -------------|  for I*\- log\- \/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + I*im|<-I*log|---------------------- + -------------|  for I*\- log\\/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + re|<-I*log|---------------------- + -------------|  for I*\- log\\/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0|
          \      2                    2           /        \      2                    2           /       ||      \             2                    2       /                                                                        |     ||      \             2                    2       /                                                                        |       ||      \           2                    2       /                                                                      |     ||      \           2                    2       /                                                                      |       ||      \            2                    2      /                                                                       |     ||      \            2                    2      /                                                                       |       ||      \          2                    2      /                                                                     |     ||      \          2                    2      /                                                                     |
                                                                                                           ||                                                                                                                          |     ||                                                                                                                          |       ||                                                                                                                      |     ||                                                                                                                      |       ||                                                                                                                       |     ||                                                                                                                       |       ||                                                                                                                   |     ||                                                                                                                   |
                                                                                                           ||                       nan                                                        otherwise                               |     ||                       nan                                                        otherwise                               |       ||                      nan                                                      otherwise                              |     ||                      nan                                                      otherwise                              |       ||                      nan                                                       otherwise                              |     ||                      nan                                                       otherwise                              |       ||                     nan                                                     otherwise                             |     ||                     nan                                                     otherwise                             |
                                                                                                           \\                                                                                                                          /     \\                                                                                                                          /       \\                                                                                                                      /     \\                                                                                                                      /       \\                                                                                                                       /     \\                                                                                                                       /       \\                                                                                                                   /     \\                                                                                                                   /

\left(\left(\left(\left(\operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} - \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) - \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} - \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) - \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(- i \log{\left(\frac{\sqrt{2} \sqrt{-5 + 3 \sqrt{5}}}{2} + \frac{i \left(3 - \sqrt{5}\right)}{2} \right)} + \left(- i \log{\left(- \frac{\sqrt{2} \sqrt{-5 + 3 \sqrt{5}}}{2} + \frac{i \left(3 - \sqrt{5}\right)}{2} \right)} + \pi\right)\right)\right) + \left(\operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} + \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) + \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} + \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) + \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)\right) + \left(\operatorname{re}{\left(\begin{cases} - i \log{\left(\frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(\frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)

         //      /    __________________                \                                                                     \       //      /    ___________________                 \                                                                      \       //      /      __________________                \                                                                       \       //      /      ___________________                 \                                                                        \                                                                                                       //      /    __________________                \                                                                     \     //      /    ___________________                 \                                                                      \     //      /      __________________                \                                                                       \     //      /      ___________________                 \                                                                        \
         ||      |   /                2                 |        /     /    __________________                \         \     |       ||      |   /                 2                  |        /     /    ___________________                 \         \    |       ||      |     /                2                 |        /     /      __________________                \         \     |       ||      |     /                 2                  |        /     /      ___________________                 \         \    |        /                         ______________\        /                         ______________\     ||      |   /                2                 |        /     /    __________________                \         \     |     ||      |   /                 2                  |        /     /    ___________________                 \         \    |     ||      |     /                2                 |        /     /      __________________                \         \     |     ||      |     /                 2                  |        /     /      ___________________                 \         \    |
         ||      |  /      /      ___\       /      ___\|        |     |   /                2                 |         |     |       ||      |  /      /      ____\       /      ____\|        |     |   /                 2                  |         |    |       ||      |    /      /      ___\       /      ___\|        |     |     /                2                 |         |     |       ||      |    /      /      ____\       /      ____\|        |     |     /                 2                  |         |    |        |  /      ___\     ___   /          ___ |        |  /      ___\     ___   /          ___ |     ||      |  /      /      ___\       /      ___\|        |     |   /                2                 |         |     |     ||      |  /      /      ____\       /      ____\|        |     |   /                 2                  |         |    |     ||      |    /      /      ___\       /      ___\|        |     |     /                2                 |         |     |     ||      |    /      /      ____\       /      ____\|        |     |     /                 2                  |         |    |
         ||      |\/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |  /      /      ___\       /      ___\|         |     |       ||      |\/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |  /      /      ____\       /      ____\|         |    |       ||      |  \/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |    /      /      ___\       /      ___\|         |     |       ||      |  \/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |    /      /      ____\       /      ____\|         |    |        |I*\3 - \/ 5 /   \/ 2 *\/  -5 + 3*\/ 5  |        |I*\3 - \/ 5 /   \/ 2 *\/  -5 + 3*\/ 5  |     ||      |\/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |  /      /      ___\       /      ___\|         |     |     ||      |\/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |  /      /      ____\       /      ____\|         |    |     ||      |  \/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |    /      /      ___\       /      ___\|         |     |     ||      |  \/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |    /      /      ____\       /      ____\|         |    |
pi + I*im|<-I*log|---------------------- + -------------|  for I*\- log\\/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + I*im|<-I*log|----------------------- - --------------|  for I*\- log\\/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + I*im|<-I*log|- ---------------------- + -------------|  for I*\- log\- \/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + I*im|<-I*log|- ----------------------- - --------------|  for I*\- log\- \/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| - I*log|------------- + -----------------------| - I*log|------------- - -----------------------| + re|<-I*log|---------------------- + -------------|  for I*\- log\\/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + re|<-I*log|----------------------- - --------------|  for I*\- log\\/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + re|<-I*log|- ---------------------- + -------------|  for I*\- log\- \/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + re|<-I*log|- ----------------------- - --------------|  for I*\- log\- \/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0|
         ||      \          2                    2      /                                                                     |       ||      \           2                    2       /                                                                      |       ||      \            2                    2      /                                                                       |       ||      \             2                    2       /                                                                        |        \      2                    2           /        \      2                    2           /     ||      \          2                    2      /                                                                     |     ||      \           2                    2       /                                                                      |     ||      \            2                    2      /                                                                       |     ||      \             2                    2       /                                                                        |
         ||                                                                                                                   |       ||                                                                                                                      |       ||                                                                                                                       |       ||                                                                                                                          |                                                                                                       ||                                                                                                                   |     ||                                                                                                                      |     ||                                                                                                                       |     ||                                                                                                                          |
         ||                     nan                                                     otherwise                             |       ||                      nan                                                      otherwise                              |       ||                      nan                                                       otherwise                              |       ||                       nan                                                        otherwise                               |                                                                                                       ||                     nan                                                     otherwise                             |     ||                      nan                                                      otherwise                              |     ||                      nan                                                       otherwise                              |     ||                       nan                                                        otherwise                               |
         \\                                                                                                                   /       \\                                                                                                                      /       \\                                                                                                                       /       \\                                                                                                                          /                                                                                                       \\                                                                                                                   /     \\                                                                                                                      /     \\                                                                                                                       /     \\                                                                                                                          /

\operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} - \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) - \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} + \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) + \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} - i \log{\left(\frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} - \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) - \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} + \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) + \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(\frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} - i \log{\left(\frac{\sqrt{2} \sqrt{-5 + 3 \sqrt{5}}}{2} + \frac{i \left(3 - \sqrt{5}\right)}{2} \right)} - i \log{\left(- \frac{\sqrt{2} \sqrt{-5 + 3 \sqrt{5}}}{2} + \frac{i \left(3 - \sqrt{5}\right)}{2} \right)} + \pi

producto

                                                                                                         /    //      /      ___________________                 \                                                                        \     //      /      ___________________                 \                                                                        \\ /    //      /    ___________________                 \                                                                      \     //      /    ___________________                 \                                                                      \\ /    //      /      __________________                \                                                                       \     //      /      __________________                \                                                                       \\ /    //      /    __________________                \                                                                     \     //      /    __________________                \                                                                     \\
     /      /                         ______________\\ /      /                         ______________\\ |    ||      |     /                 2                  |        /     /      ___________________                 \         \    |     ||      |     /                 2                  |        /     /      ___________________                 \         \    || |    ||      |   /                 2                  |        /     /    ___________________                 \         \    |     ||      |   /                 2                  |        /     /    ___________________                 \         \    || |    ||      |     /                2                 |        /     /      __________________                \         \     |     ||      |     /                2                 |        /     /      __________________                \         \     || |    ||      |   /                2                 |        /     /    __________________                \         \     |     ||      |   /                2                 |        /     /    __________________                \         \     ||
     |      |  /      ___\     ___   /          ___ || |      |  /      ___\     ___   /          ___ || |    ||      |    /      /      ____\       /      ____\|        |     |     /                 2                  |         |    |     ||      |    /      /      ____\       /      ____\|        |     |     /                 2                  |         |    || |    ||      |  /      /      ____\       /      ____\|        |     |   /                 2                  |         |    |     ||      |  /      /      ____\       /      ____\|        |     |   /                 2                  |         |    || |    ||      |    /      /      ___\       /      ___\|        |     |     /                2                 |         |     |     ||      |    /      /      ___\       /      ___\|        |     |     /                2                 |         |     || |    ||      |  /      /      ___\       /      ___\|        |     |   /                2                 |         |     |     ||      |  /      /      ___\       /      ___\|        |     |   /                2                 |         |     ||
     |      |I*\3 - \/ 5 /   \/ 2 *\/  -5 + 3*\/ 5  || |      |I*\3 - \/ 5 /   \/ 2 *\/  -5 + 3*\/ 5  || |    ||      |  \/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |    /      /      ____\       /      ____\|         |    |     ||      |  \/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |    /      /      ____\       /      ____\|         |    || |    ||      |\/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |  /      /      ____\       /      ____\|         |    |     ||      |\/   4 - \3 + \/ 21 /     I*\3 + \/ 21 /|        |     |  /      /      ____\       /      ____\|         |    || |    ||      |  \/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |    /      /      ___\       /      ___\|         |     |     ||      |  \/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |    /      /      ___\       /      ___\|         |     || |    ||      |\/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |  /      /      ___\       /      ___\|         |     |     ||      |\/   4 - \3 + \/ 5 /     I*\3 + \/ 5 /|        |     |  /      /      ___\       /      ___\|         |     ||
0*pi*|-I*log|------------- - -----------------------||*|-I*log|------------- + -----------------------||*|I*im|<-I*log|- ----------------------- - --------------|  for I*\- log\- \/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + re|<-I*log|- ----------------------- - --------------|  for I*\- log\- \/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0||*|I*im|<-I*log|----------------------- - --------------|  for I*\- log\\/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0| + re|<-I*log|----------------------- - --------------|  for I*\- log\\/   4 - \3 + \/ 21 /   - I*\3 + \/ 21 // + log(2)/ < 0||*|I*im|<-I*log|- ---------------------- + -------------|  for I*\- log\- \/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + re|<-I*log|- ---------------------- + -------------|  for I*\- log\- \/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0||*|I*im|<-I*log|---------------------- + -------------|  for I*\- log\\/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0| + re|<-I*log|---------------------- + -------------|  for I*\- log\\/   4 - \3 + \/ 5 /   + I*\3 + \/ 5 // + log(2)/ >= 0||
     \      \      2                    2           // \      \      2                    2           // |    ||      \             2                    2       /                                                                        |     ||      \             2                    2       /                                                                        || |    ||      \           2                    2       /                                                                      |     ||      \           2                    2       /                                                                      || |    ||      \            2                    2      /                                                                       |     ||      \            2                    2      /                                                                       || |    ||      \          2                    2      /                                                                     |     ||      \          2                    2      /                                                                     ||
                                                                                                         |    ||                                                                                                                          |     ||                                                                                                                          || |    ||                                                                                                                      |     ||                                                                                                                      || |    ||                                                                                                                       |     ||                                                                                                                       || |    ||                                                                                                                   |     ||                                                                                                                   ||
                                                                                                         |    ||                       nan                                                        otherwise                               |     ||                       nan                                                        otherwise                               || |    ||                      nan                                                      otherwise                              |     ||                      nan                                                      otherwise                              || |    ||                      nan                                                       otherwise                              |     ||                      nan                                                       otherwise                              || |    ||                     nan                                                     otherwise                             |     ||                     nan                                                     otherwise                             ||
                                                                                                         \    \\                                                                                                                          /     \\                                                                                                                          // \    \\                                                                                                                      /     \\                                                                                                                      // \    \\                                                                                                                       /     \\                                                                                                                       // \    \\                                                                                                                   /     \\                                                                                                                   //

- i \log{\left(\frac{\sqrt{2} \sqrt{-5 + 3 \sqrt{5}}}{2} + \frac{i \left(3 - \sqrt{5}\right)}{2} \right)} 0 \pi \left(- i \log{\left(- \frac{\sqrt{2} \sqrt{-5 + 3 \sqrt{5}}}{2} + \frac{i \left(3 - \sqrt{5}\right)}{2} \right)}\right) \left(\operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} - \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) - \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} - \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) - \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} + \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) + \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{i \left(3 + \sqrt{21}\right)}{2} + \frac{\sqrt{4 - \left(3 + \sqrt{21}\right)^{2}}}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- i \left(3 + \sqrt{21}\right) + \sqrt{4 - \left(3 + \sqrt{21}\right)^{2}} \right)}\right) < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - i \log{\left(- \frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(- \frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(- \sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} - i \log{\left(\frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} - i \log{\left(\frac{\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}}}{2} + \frac{i \left(\sqrt{5} + 3\right)}{2} \right)} & \text{for}\: i \left(\log{\left(2 \right)} - \log{\left(\sqrt{4 - \left(\sqrt{5} + 3\right)^{2}} + i \left(\sqrt{5} + 3\right) \right)}\right) \geq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)

0

Respuesta numérica [src]

x1 = -97.3893722612836

x2 = -43.9822971502571

x3 = 56.5486677646163

x4 = -48.0368021801426

x5 = 28.2743338823081

x6 = -81.6814089933346

x7 = -15.707963267949

x8 = 72.2566310325652

x9 = -106.814150222053

x10 = 63.2237757472427

x11 = -53.4070751110265

x12 = 15.3160405925021

x13 = -18.8495559215388

x14 = 25.1327412287183

x15 = 100.530964914873

x16 = 81.6814089933346

x17 = 69.1150383789755

x18 = 69.5069610544223

x19 = -17.936643545243

x20 = -21.9911485751286

x21 = -78.5398163397448

x22 = 34.1655965140408

x23 = 2.74966997814292

x24 = 53.4070751110265

x25 = -30.5030141596022

x26 = -91.106186954104

x27 = -72.2566310325652

x28 = -11.6534582380634

x29 = 40.4487818212204

x30 = 15.707963267949

x31 = 50.2654824574367

x32 = 40.8407044966673

x33 = -35.4704315657835

x34 = -28.2743338823081

x35 = -62.8318530717959

x36 = -6.28318530717959

x37 = 3.14159265358979

x38 = -25.1327412287183

x39 = -61.9189406955001

x40 = -84.8230016469244

x41 = -85.7359140232202

x42 = -87.9645943005142

x43 = -74.4853113098593

x44 = -34.5575191894877

x45 = 25.5246639041652

x46 = 0.0

x47 = 31.4159265358979

x48 = -68.2021260026797

x49 = -65.9734457253857

x50 = 47.1238898038469

x51 = 18.8495559215388

x52 = 84.8230016469244

x53 = 84.4310789714775

x54 = 91.106186954104

x55 = 6.28318530717959

x56 = -47.1238898038469

x57 = 94.2477796076938

x58 = 65.9734457253857

x59 = -56.5486677646163

x60 = -41.7536168729631

x61 = 21.9911485751286

x62 = -24.2198288524226

x63 = 75.7901463616019

x64 = 90.7142642786571

x65 = 46.7319671284

x66 = 31.8078492113448

x67 = 75.398223686155

x68 = 87.9645943005142

x69 = 12.5663706143592

x70 = -3.14159265358979

x71 = -37.6991118430775

x72 = -12.5663706143592

x73 = 97.3893722612836

x74 = 78.147893664298

x75 = -10.3376903370651

x76 = 59.6902604182061

x77 = 38.0910345185244

x78 = 96.9974495858367

x79 = -99.6180525385776

x80 = 9.0328552853225

x81 = 43.9822971502571

x82 = -50.2654824574367

x83 = 37.6991118430775

x84 = -40.8407044966673

x85 = -59.6902604182061

x86 = -79.4527287160406

x87 = 53.0151524355796

x88 = -75.398223686155

x89 = -69.1150383789755

x90 = 9.42477796076938

x91 = 19.2414785969856

x92 = -4.05450502988554

x93 = 62.8318530717959

x94 = -92.0190993303998

x95 = 82.0733316687815

x96 = -55.6357553883205

x97 = 59.2983377427592

x98 = -94.2477796076938

x99 = -31.4159265358979

x99 = -31.4159265358979

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Solución