(4-6sinx)tgx=2sin|x|cosx la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Gráfica
/ ______________\
| / ___\ ___ / ___ |
|I*\3 - \/ 5 / \/ 2 *\/ -5 + 3*\/ 5 |
x3 = -I*log|------------- - -----------------------|
\ 2 2 /
x3=−ilog(−22−5+35+2i(3−5))
/ ______________\
| / ___\ ___ / ___ |
|I*\3 - \/ 5 / \/ 2 *\/ -5 + 3*\/ 5 |
x4 = -I*log|------------- + -----------------------|
\ 2 2 /
x4=−ilog(22−5+35+2i(3−5))
// / ___________________ \ \ // / ___________________ \ \
|| | / 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 |
\\ / \\ /
x5=re⎩⎨⎧−ilog(−2i(3+21)−24−(3+21)2)NaNfori(log(2)−log(−i(3+21)−4−(3+21)2))<0otherwise+iim⎩⎨⎧−ilog(−2i(3+21)−24−(3+21)2)NaNfori(log(2)−log(−i(3+21)−4−(3+21)2))<0otherwise
// / ___________________ \ \ // / ___________________ \ \
|| | / 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 |
\\ / \\ /
x6=re⎩⎨⎧−ilog(−2i(3+21)+24−(3+21)2)NaNfori(log(2)−log(−i(3+21)+4−(3+21)2))<0otherwise+iim⎩⎨⎧−ilog(−2i(3+21)+24−(3+21)2)NaNfori(log(2)−log(−i(3+21)+4−(3+21)2))<0otherwise
// / __________________ \ \ // / __________________ \ \
|| | / 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 |
\\ / \\ /
x7=re⎩⎨⎧−ilog(−24−(5+3)2+2i(5+3))NaNfori(log(2)−log(−4−(5+3)2+i(5+3)))≥0otherwise+iim⎩⎨⎧−ilog(−24−(5+3)2+2i(5+3))NaNfori(log(2)−log(−4−(5+3)2+i(5+3)))≥0otherwise
// / __________________ \ \ // / __________________ \ \
|| | / 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 |
\\ / \\ /
x8=re⎩⎨⎧−ilog(24−(5+3)2+2i(5+3))NaNfori(log(2)−log(4−(5+3)2+i(5+3)))≥0otherwise+iim⎩⎨⎧−ilog(24−(5+3)2+2i(5+3))NaNfori(log(2)−log(4−(5+3)2+i(5+3)))≥0otherwise
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]
// / ___________________ \ \ // / ___________________ \ \ // / ___________________ \ \ // / ___________________ \ \ // / __________________ \ \ // / __________________ \ \ // / __________________ \ \ // / __________________ \ \
/ ______________\ / ______________\ || | / 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 |
\\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ /
re⎩⎨⎧−ilog(−2i(3+21)−24−(3+21)2)NaNfori(log(2)−log(−i(3+21)−4−(3+21)2))<0otherwise+iim⎩⎨⎧−ilog(−2i(3+21)−24−(3+21)2)NaNfori(log(2)−log(−i(3+21)−4−(3+21)2))<0otherwise+(−ilog(22−5+35+2i(3−5))+(−ilog(−22−5+35+2i(3−5))+π))+re⎩⎨⎧−ilog(−2i(3+21)+24−(3+21)2)NaNfori(log(2)−log(−i(3+21)+4−(3+21)2))<0otherwise+iim⎩⎨⎧−ilog(−2i(3+21)+24−(3+21)2)NaNfori(log(2)−log(−i(3+21)+4−(3+21)2))<0otherwise+re⎩⎨⎧−ilog(−24−(5+3)2+2i(5+3))NaNfori(log(2)−log(−4−(5+3)2+i(5+3)))≥0otherwise+iim⎩⎨⎧−ilog(−24−(5+3)2+2i(5+3))NaNfori(log(2)−log(−4−(5+3)2+i(5+3)))≥0otherwise+re⎩⎨⎧−ilog(24−(5+3)2+2i(5+3))NaNfori(log(2)−log(4−(5+3)2+i(5+3)))≥0otherwise+iim⎩⎨⎧−ilog(24−(5+3)2+2i(5+3))NaNfori(log(2)−log(4−(5+3)2+i(5+3)))≥0otherwise
// / __________________ \ \ // / ___________________ \ \ // / __________________ \ \ // / ___________________ \ \ // / __________________ \ \ // / ___________________ \ \ // / __________________ \ \ // / ___________________ \ \
|| | / 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 |
\\ / \\ / \\ / \\ / \\ / \\ / \\ / \\ /
re⎩⎨⎧−ilog(−2i(3+21)−24−(3+21)2)NaNfori(log(2)−log(−i(3+21)−4−(3+21)2))<0otherwise+re⎩⎨⎧−ilog(−2i(3+21)+24−(3+21)2)NaNfori(log(2)−log(−i(3+21)+4−(3+21)2))<0otherwise+re⎩⎨⎧−ilog(−24−(5+3)2+2i(5+3))NaNfori(log(2)−log(−4−(5+3)2+i(5+3)))≥0otherwise+re⎩⎨⎧−ilog(24−(5+3)2+2i(5+3))NaNfori(log(2)−log(4−(5+3)2+i(5+3)))≥0otherwise+iim⎩⎨⎧−ilog(−2i(3+21)−24−(3+21)2)NaNfori(log(2)−log(−i(3+21)−4−(3+21)2))<0otherwise+iim⎩⎨⎧−ilog(−2i(3+21)+24−(3+21)2)NaNfori(log(2)−log(−i(3+21)+4−(3+21)2))<0otherwise+iim⎩⎨⎧−ilog(−24−(5+3)2+2i(5+3))NaNfori(log(2)−log(−4−(5+3)2+i(5+3)))≥0otherwise+iim⎩⎨⎧−ilog(24−(5+3)2+2i(5+3))NaNfori(log(2)−log(4−(5+3)2+i(5+3)))≥0otherwise−ilog(22−5+35+2i(3−5))−ilog(−22−5+35+2i(3−5))+π
/ // / ___________________ \ \ // / ___________________ \ \\ / // / ___________________ \ \ // / ___________________ \ \\ / // / __________________ \ \ // / __________________ \ \\ / // / __________________ \ \ // / __________________ \ \\
/ / ______________\\ / / ______________\\ | || | / 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 ||
\ \\ / \\ // \ \\ / \\ // \ \\ / \\ // \ \\ / \\ //
−ilog(22−5+35+2i(3−5))0π(−ilog(−22−5+35+2i(3−5)))re⎩⎨⎧−ilog(−2i(3+21)−24−(3+21)2)NaNfori(log(2)−log(−i(3+21)−4−(3+21)2))<0otherwise+iim⎩⎨⎧−ilog(−2i(3+21)−24−(3+21)2)NaNfori(log(2)−log(−i(3+21)−4−(3+21)2))<0otherwisere⎩⎨⎧−ilog(−2i(3+21)+24−(3+21)2)NaNfori(log(2)−log(−i(3+21)+4−(3+21)2))<0otherwise+iim⎩⎨⎧−ilog(−2i(3+21)+24−(3+21)2)NaNfori(log(2)−log(−i(3+21)+4−(3+21)2))<0otherwisere⎩⎨⎧−ilog(−24−(5+3)2+2i(5+3))NaNfori(log(2)−log(−4−(5+3)2+i(5+3)))≥0otherwise+iim⎩⎨⎧−ilog(−24−(5+3)2+2i(5+3))NaNfori(log(2)−log(−4−(5+3)2+i(5+3)))≥0otherwisere⎩⎨⎧−ilog(24−(5+3)2+2i(5+3))NaNfori(log(2)−log(4−(5+3)2+i(5+3)))≥0otherwise+iim⎩⎨⎧−ilog(24−(5+3)2+2i(5+3))NaNfori(log(2)−log(4−(5+3)2+i(5+3)))≥0otherwise