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- La ecuación:
-
Ecuación x^2-4x+5=0
-
Ecuación x^2+3x+2=0
-
Ecuación -25-x=-17
-
Ecuación x^2+3x=4
- Expresar {x} en función de y en la ecuación:
- 10*x-2*y=0
- 1*x+4*y=20
- 3*x-7*y=13
- 13*x-15*y=-6
-
Expresiones idénticas
- cosx*cos2x*cos4x= cero . ciento veinticinco
- coseno de x multiplicar por coseno de 2x multiplicar por coseno de 4x es igual a 0.125
- coseno de x multiplicar por coseno de 2x multiplicar por coseno de 4x es igual a cero . ciento veinticinco
- cosxcos2xcos4x=0.125
- cosx*cos2x*cos4x=O.125
-
Expresiones con funciones
- cosx
- cosx*cosx+(x-Pi/2)^(1/2)*cosx+(x-Pi/2)^(1/2)=0
- cosx/1+sinx=0
- cosx3=-12
- cosx=c+2
- cosx/5=-(√3/2)
cosx*cos2x*cos4x=0.125 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
cos(x)*cos(2*x)*cos(4*x) = 1/8
$$\cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(4 x \right)} = \frac{1}{8}$$
Suma y producto de raíces
[src]
suma
/ /pi\\ / /pi\\ / /pi\\ / /pi\\
/ _____________________\ |cos|--|| |cos|--|| / _____________________\ / _____________________\ |cos|--|| |cos|--|| / _____________________\
pi 2*pi pi pi 2*pi pi 7*pi 6*pi / 7 ____\ / 2/9\ | / 2/pi\ 2/pi\ | | \18/| | \18/| | / 2/pi\ 2/pi\ | | / 2/pi\ 2/pi\ | | \14/| | \14/| | / 2/pi\ 2/pi\ |
- -- - ---- - -- + -- + ---- + -- + ---- + ---- - I*log\-\/ -1 / - I*log\-(-1) / + -pi - I*log| / cos |--| + sin |--| | + atan|-------| + pi - atan|-------| - I*log| / cos |--| + sin |--| | + -pi - I*log| / cos |--| + sin |--| | + atan|-------| + pi - atan|-------| - I*log| / cos |--| + sin |--| |
3 7 9 9 7 3 9 7 \\/ \18/ \18/ / | /pi\| | /pi\| \\/ \18/ \18/ / \\/ \14/ \14/ / | /pi\| | /pi\| \\/ \14/ \14/ /
|sin|--|| |sin|--|| |sin|--|| |sin|--||
\ \18// \ \18// \ \14// \ \14//
$$\left(\left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)}\right) + \left(\left(\left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right) + \left(- i \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)} + \left(- i \log{\left(- \sqrt[7]{-1} \right)} + \left(\left(\left(\left(\left(\left(\left(- \frac{\pi}{3} - \frac{2 \pi}{7}\right) - \frac{\pi}{9}\right) + \frac{\pi}{9}\right) + \frac{2 \pi}{7}\right) + \frac{\pi}{3}\right) + \frac{7 \pi}{9}\right) + \frac{6 \pi}{7}\right)\right)\right)\right) + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \pi\right)\right)\right) + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \pi\right)$$
=
/ _____________________\ / _____________________\ 103*pi / 7 ____\ / 2/9\ | / 2/pi\ 2/pi\ | | / 2/pi\ 2/pi\ | ------ - I*log\-\/ -1 / - I*log\-(-1) / - 2*I*log| / cos |--| + sin |--| | - 2*I*log| / cos |--| + sin |--| | 63 \\/ \14/ \14/ / \\/ \18/ \18/ /
$$- i \log{\left(- \sqrt[7]{-1} \right)} - i \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)} - 2 i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} - 2 i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \frac{103 \pi}{63}$$
producto
/ / /pi\\\ / / /pi\\ \ / / /pi\\\ / / /pi\\ \
| / _____________________\ |cos|--||| | |cos|--|| / _____________________\| | / _____________________\ |cos|--||| | |cos|--|| / _____________________\|
-pi -2*pi -pi pi 2*pi pi 7*pi 6*pi / / 7 ____\\ / / 2/9\\ | | / 2/pi\ 2/pi\ | | \18/|| | | \18/| | / 2/pi\ 2/pi\ || | | / 2/pi\ 2/pi\ | | \14/|| | | \14/| | / 2/pi\ 2/pi\ ||
----*-----*----*--*----*--*----*----*\-I*log\-\/ -1 //*\-I*log\-(-1) //*|-pi - I*log| / cos |--| + sin |--| | + atan|-------||*|pi - atan|-------| - I*log| / cos |--| + sin |--| ||*|-pi - I*log| / cos |--| + sin |--| | + atan|-------||*|pi - atan|-------| - I*log| / cos |--| + sin |--| ||
3 7 9 9 7 3 9 7 | \\/ \18/ \18/ / | /pi\|| | | /pi\| \\/ \18/ \18/ /| | \\/ \14/ \14/ / | /pi\|| | | /pi\| \\/ \14/ \14/ /|
| |sin|--||| | |sin|--|| | | |sin|--||| | |sin|--|| |
\ \ \18/// \ \ \18// / \ \ \14/// \ \ \14// /
$$- i \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)} - i \log{\left(- \sqrt[7]{-1} \right)} \frac{6 \pi}{7} \frac{7 \pi}{9} \frac{\pi}{3} \frac{2 \pi}{7} \frac{\pi}{9} \cdot - \frac{\pi}{9} \cdot - \frac{\pi}{3} \left(- \frac{2 \pi}{7}\right) \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \pi\right) \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \pi\right)$$
=
12 / 7 ____\ / 2/9\
3200*pi *log\-\/ -1 /*log\-(-1) /
------------------------------------
425329947
$$\frac{3200 \pi^{12} \log{\left(- \sqrt[7]{-1} \right)} \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)}}{425329947}$$
3200*pi^12*log(-(-1)^(1/7))*log(-(-1)^(2/9))/425329947
Respuesta rápida
[src]
-pi
x1 = ----
3
$$x_{1} = - \frac{\pi}{3}$$
-2*pi
x2 = -----
7
$$x_{2} = - \frac{2 \pi}{7}$$
-pi
x3 = ----
9
$$x_{3} = - \frac{\pi}{9}$$
pi
x4 = --
9
$$x_{4} = \frac{\pi}{9}$$
2*pi
x5 = ----
7
$$x_{5} = \frac{2 \pi}{7}$$
pi
x6 = --
3
$$x_{6} = \frac{\pi}{3}$$
7*pi
x7 = ----
9
$$x_{7} = \frac{7 \pi}{9}$$
6*pi
x8 = ----
7
$$x_{8} = \frac{6 \pi}{7}$$
/ 7 ____\ x9 = -I*log\-\/ -1 /
$$x_{9} = - i \log{\left(- \sqrt[7]{-1} \right)}$$
/ 2/9\ x10 = -I*log\-(-1) /
$$x_{10} = - i \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)}$$
/ /pi\\
/ _____________________\ |cos|--||
| / 2/pi\ 2/pi\ | | \18/|
x11 = -pi - I*log| / cos |--| + sin |--| | + atan|-------|
\\/ \18/ \18/ / | /pi\|
|sin|--||
\ \18//
$$x_{11} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}$$
/ /pi\\
|cos|--|| / _____________________\
| \18/| | / 2/pi\ 2/pi\ |
x12 = pi - atan|-------| - I*log| / cos |--| + sin |--| |
| /pi\| \\/ \18/ \18/ /
|sin|--||
\ \18//
$$x_{12} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \pi$$
/ /pi\\
/ _____________________\ |cos|--||
| / 2/pi\ 2/pi\ | | \14/|
x13 = -pi - I*log| / cos |--| + sin |--| | + atan|-------|
\\/ \14/ \14/ / | /pi\|
|sin|--||
\ \14//
$$x_{13} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)}$$
/ /pi\\
|cos|--|| / _____________________\
| \14/| | / 2/pi\ 2/pi\ |
x14 = pi - atan|-------| - I*log| / cos |--| + sin |--| |
| /pi\| \\/ \14/ \14/ /
|sin|--||
\ \14//
$$x_{14} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \pi$$
x14 = -atan(cos(pi/14)/sin(pi/14)) - i*log(sqrt(sin(pi/14)^2 + cos(pi/14)^2)) + pi
Respuesta numérica
[src]
x1 = 61.9342551707702
x2 = 45.0294947014537
x3 = 85.2718005974372
x4 = -91.8043186549017
x5 = 68.2174404779498
x6 = 35.9537825910832
x7 = 98.0875039620813
x8 = -13.4639685153848
x9 = -43.6332312998582
x10 = 49.9164166070378
x11 = -65.2753140245879
x12 = 0.349065850398866
x13 = -1.74532925199433
x14 = -26.030339129744
x15 = -11.6687727133335
x16 = -9.87357691128221
x17 = 27.5762021815104
x18 = 63.8790506229925
x19 = -3.83972435438753
x20 = -71.8078320820524
x21 = -93.8987137572949
x22 = 52.010811709431
x23 = -75.7472895365539
x24 = 38.0481776934764
x25 = 49.367884556411
x26 = 71.8078320820524
x27 = -53.8558740615393
x28 = -49.9164166070378
x29 = -19.7471538225644
x30 = -99.6333670138477
x31 = 84.1248699461267
x32 = -61.7846555205993
x33 = 24.2351433276927
x34 = 58.2939970166106
x35 = 79.9360797413403
x36 = 8.02851455917392
x37 = -29.6705972839036
x38 = -5.93411945678072
x39 = 100.181899064475
x40 = 70.0126362800011
x41 = -45.7276264022514
x42 = -24.0855436775217
x43 = 12.2173047639603
x44 = -42.2369678982628
x45 = -70.0126362800011
x46 = 40.1425727958696
x47 = 78.091017389232
x48 = 93.8987137572949
x49 = -55.6510698635906
x50 = 19.8967534727354
x51 = -86.2192650485199
x52 = -31.7649923862968
x53 = 22.4399475256414
x54 = 5.93411945678072
x55 = -63.7294509728215
x56 = -77.8416846389471
x57 = -21.5423496246157
x58 = 17.9519580205131
x59 = 56.1996019142174
x60 = 82.0304748437335
x61 = 74.3510261349584
x62 = 95.9931088596881
x63 = 44.331363000656
x64 = 76.2958215871807
x65 = 86.2192650485199
x66 = -83.4766047953859
x67 = -87.6155284501153
x68 = -33.85938748869
x69 = -168.598805742652
x70 = -52.010811709431
x71 = 10.1229096615671
x72 = 60.1390593687189
x73 = 111.302139727181
x74 = 54.1052068118242
x75 = -95.9931088596881
x76 = 91.5549859046168
x77 = 14.3116998663535
x78 = -89.7597901025655
x79 = -68.0678408277789
x80 = -8.02851455917392
x81 = 34.1087202389749
x82 = -97.8381712117964
x83 = 66.4222446758985
x84 = 27.8255349317953
x85 = 88.3136601509131
x86 = 32.3135244369236
x87 = 16.1567622184618
x88 = 29.6705972839036
x89 = -73.6528944341607
x90 = -16.1567622184618
x91 = -27.8255349317953
x92 = -60.1390593687189
x93 = -82.0304748437335
x94 = -35.9537825910832
x95 = -47.8220215046446
x96 = -77.1435529381494
x97 = -24.2351433276927
x98 = 42.2369678982628
x99 = -38.0481776934764
x99 = -38.0481776934764