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Expresiones con funciones
- cosx
- cosx+4cos2x=0
- cosx-2|cosx|=y
- Módulo |
- |x|=4
- |x+1|-|x|+3|x-1|-2|x-2|=x+2
- |x+3|=a
- |x|=4,5
- |x|=x
(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)
$$\left(4 - 6 \sin{\left(x \right)}\right) \tan{\left(x \right)} = 2 \sin{\left(\left|{x}\right| \right)} \cos{\left(x \right)}$$
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
$$0$$
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