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- La ecuación:
-
Ecuación x^3-x^2-x-1=0
-
Ecuación 3x-2(3x+4)=10
-
Ecuación 12-4(x-3)=39-9x
-
Ecuación 0,2x+2,7=1,4-1,1x
- Expresar {x} en función de y en la ecuación:
- -11*x-3*y=14
- 2*x-15*y=-1
- -18*x-6*y=-1
- 6*x+9*y=-9
-
Expresiones idénticas
- cos(siete *x)+cos(x)= cero
- coseno de (7 multiplicar por x) más coseno de (x) es igual a 0
- coseno de (siete multiplicar por x) más coseno de (x) es igual a cero
- cos(7x)+cos(x)=0
- cos7x+cosx=0
- cos(7*x)+cos(x)=O
-
Expresiones semejantes
- cos(7*x)-cos(x)=0
- cos7(x)+cos(x)=0
- cos7x+cosx=2cos3x(sin2x-1)
- cos(7*x)+cosx=0
-
Expresiones con funciones
- Coseno cos
- cos(x)=-3
- cos(0.5-y)-0.5y+2=0
- cos(2*x-pi/4)=0
- cos(x)=-(2/5)
- cos(x)^2=-1
- Coseno cos
- cos(x)=-3
- cos(0.5-y)-0.5y+2=0
- cos(2*x-pi/4)=0
- cos(x)=-(2/5)
- cos(x)^2=-1
cos(7*x)+cos(x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Respuesta rápida
[src]
-7*pi
x1 = -----
8
$$x_{1} = - \frac{7 \pi}{8}$$
-5*pi
x2 = -----
6
$$x_{2} = - \frac{5 \pi}{6}$$
-pi
x3 = ----
2
$$x_{3} = - \frac{\pi}{2}$$
-3*pi
x4 = -----
8
$$x_{4} = - \frac{3 \pi}{8}$$
-pi
x5 = ----
6
$$x_{5} = - \frac{\pi}{6}$$
pi
x6 = --
8
$$x_{6} = \frac{\pi}{8}$$
pi
x7 = --
6
$$x_{7} = \frac{\pi}{6}$$
pi
x8 = --
2
$$x_{8} = \frac{\pi}{2}$$
5*pi
x9 = ----
8
$$x_{9} = \frac{5 \pi}{8}$$
5*pi
x10 = ----
6
$$x_{10} = \frac{5 \pi}{6}$$
/ ___________ ___________\
| / ___ / ___ |
/log(8) / ___\\ |\/ 2 + \/ 2 + \/ 2 - \/ 2 |
x11 = I*|------ - log\2*\/ 2 /| + atan|-------------------------------|
\ 2 / | ___________ ___________|
| / ___ / ___ |
\\/ 2 + \/ 2 - \/ 2 - \/ 2 /
$$x_{11} = \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
/ ___________ ___________\
| / ___ / ___ |
/log(8) / ___\\ |\/ 2 - \/ 2 - \/ 2 + \/ 2 |
x12 = I*|------ - log\2*\/ 2 /| + atan|-------------------------------|
\ 2 / | ___________ ___________|
| / ___ / ___ |
\\/ 2 + \/ 2 + \/ 2 - \/ 2 /
$$x_{12} = \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
/ ___________ ___________ \
| / ___ / ___ |
/log(8) / ___\\ | \/ 2 + \/ 2 - \/ 2 - \/ 2 |
x13 = pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------|
\ 2 / | ___________ ___________|
| / ___ / ___ |
\- \/ 2 + \/ 2 - \/ 2 - \/ 2 /
$$x_{13} = \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
/ / ___________ ___________\ \
| | / ___ / ___ | |
|-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | /log(8) / ___\\
x14 = -pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /|
| ___________ ___________ | \ 2 /
| / ___ / ___ |
\ \/ 2 - \/ 2 - \/ 2 + \/ 2 /
$$x_{14} = - \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
x14 = -pi - atan(-(-sqrt(sqrt(2) + 2) - sqrt(2 - sqrt(2)))/(-sqrt(sqrt(2) + 2) + sqrt(2 - sqrt(2)))) + i*(-log(2*sqrt(2)) + log(8)/2)
Suma y producto de raíces
[src]
suma
/ ___________ ___________\ / ___________ ___________\ / ___________ ___________ \ / / ___________ ___________\ \
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | | / ___ / ___ | |
7*pi 5*pi pi 3*pi pi pi pi pi 5*pi 5*pi /log(8) / ___\\ |\/ 2 + \/ 2 + \/ 2 - \/ 2 | /log(8) / ___\\ |\/ 2 - \/ 2 - \/ 2 + \/ 2 | /log(8) / ___\\ | \/ 2 + \/ 2 - \/ 2 - \/ 2 | |-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | /log(8) / ___\\
- ---- - ---- - -- - ---- - -- + -- + -- + -- + ---- + ---- + I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------| + -pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /|
8 6 2 8 6 8 6 2 8 6 \ 2 / | ___________ ___________| \ 2 / | ___________ ___________| \ 2 / | ___________ ___________| | ___________ ___________ | \ 2 /
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ |
\\/ 2 + \/ 2 - \/ 2 - \/ 2 / \\/ 2 + \/ 2 + \/ 2 - \/ 2 / \- \/ 2 + \/ 2 - \/ 2 - \/ 2 / \ \/ 2 - \/ 2 - \/ 2 + \/ 2 /
$$\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(- \frac{7 \pi}{8} - \frac{5 \pi}{6}\right) - \frac{\pi}{2}\right) - \frac{3 \pi}{8}\right) - \frac{\pi}{6}\right) + \frac{\pi}{8}\right) + \frac{\pi}{6}\right) + \frac{\pi}{2}\right) + \frac{5 \pi}{8}\right) + \frac{5 \pi}{6}\right) + \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)\right) + \left(- \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)$$
=
/ / ___________ ___________\ \ / ___________ ___________\ / ___________ ___________\ / ___________ ___________ \
| | / ___ / ___ | | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ |
|-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | pi /log(8) / ___\\ |\/ 2 - \/ 2 - \/ 2 + \/ 2 | |\/ 2 + \/ 2 + \/ 2 - \/ 2 | | \/ 2 + \/ 2 - \/ 2 - \/ 2 |
- atan|-------------------------------------| - -- + 4*I*|------ - log\2*\/ 2 /| + atan|-------------------------------| + atan|-------------------------------| + atan|---------------------------------|
| ___________ ___________ | 2 \ 2 / | ___________ ___________| | ___________ ___________| | ___________ ___________|
| / ___ / ___ | | / ___ / ___ | | / ___ / ___ | | / ___ / ___ |
\ \/ 2 - \/ 2 - \/ 2 + \/ 2 / \\/ 2 + \/ 2 + \/ 2 - \/ 2 / \\/ 2 + \/ 2 - \/ 2 - \/ 2 / \- \/ 2 + \/ 2 - \/ 2 - \/ 2 /
$$- \frac{\pi}{2} + \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + \operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + 4 i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)$$
producto
/ / ___________ ___________\\ / / ___________ ___________\\ / / ___________ ___________ \\ / / / ___________ ___________\ \ \
| | / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ || | | | / ___ / ___ | | |
-7*pi -5*pi -pi -3*pi -pi pi pi pi 5*pi 5*pi | /log(8) / ___\\ |\/ 2 + \/ 2 + \/ 2 - \/ 2 || | /log(8) / ___\\ |\/ 2 - \/ 2 - \/ 2 + \/ 2 || | /log(8) / ___\\ | \/ 2 + \/ 2 - \/ 2 - \/ 2 || | |-\- \/ 2 + \/ 2 - \/ 2 - \/ 2 / | /log(8) / ___\\|
-----*-----*----*-----*----*--*--*--*----*----*|I*|------ - log\2*\/ 2 /| + atan|-------------------------------||*|I*|------ - log\2*\/ 2 /| + atan|-------------------------------||*|pi + I*|------ - log\2*\/ 2 /| + atan|---------------------------------||*|-pi - atan|-------------------------------------| + I*|------ - log\2*\/ 2 /||
8 6 2 8 6 8 6 2 8 6 | \ 2 / | ___________ ___________|| | \ 2 / | ___________ ___________|| | \ 2 / | ___________ ___________|| | | ___________ ___________ | \ 2 /|
| | / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ || | | / ___ / ___ | |
\ \\/ 2 + \/ 2 - \/ 2 - \/ 2 // \ \\/ 2 + \/ 2 + \/ 2 - \/ 2 // \ \- \/ 2 + \/ 2 - \/ 2 - \/ 2 // \ \ \/ 2 - \/ 2 - \/ 2 + \/ 2 / /
$$\frac{5 \pi}{6} \frac{5 \pi}{8} \frac{\pi}{2} \frac{\pi}{6} \frac{\pi}{8} \cdot - \frac{\pi}{6} \cdot - \frac{3 \pi}{8} \cdot - \frac{\pi}{2} \cdot - \frac{7 \pi}{8} \left(- \frac{5 \pi}{6}\right) \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{- \sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}} \right)} + \pi + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right) \left(- \pi - \operatorname{atan}{\left(- \frac{- \sqrt{\sqrt{2} + 2} - \sqrt{2 - \sqrt{2}}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + i \left(- \log{\left(2 \sqrt{2} \right)} + \frac{\log{\left(8 \right)}}{2}\right)\right)$$
=
/ / ___________ ___________\\ / / ___________ ___________\\ / ___________ ___________\ / ___________ ___________\
| | / ___ / ___ || | | / ___ / ___ || | / ___ / ___ | | / ___ / ___ |
10 | |\/ 2 - \/ 2 - \/ 2 + \/ 2 || | |\/ 2 + \/ 2 + \/ 2 - \/ 2 || |\/ 2 - \/ 2 - \/ 2 + \/ 2 | |\/ 2 + \/ 2 + \/ 2 - \/ 2 |
-875*pi *|pi + atan|-------------------------------||*|pi + atan|-------------------------------||*atan|-------------------------------|*atan|-------------------------------|
| | ___________ ___________|| | | ___________ ___________|| | ___________ ___________| | ___________ ___________|
| | / ___ / ___ || | | / ___ / ___ || | / ___ / ___ | | / ___ / ___ |
\ \\/ 2 + \/ 2 + \/ 2 - \/ 2 // \ \\/ 2 - \/ 2 - \/ 2 + \/ 2 // \\/ 2 + \/ 2 + \/ 2 - \/ 2 / \\/ 2 - \/ 2 - \/ 2 + \/ 2 /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
7077888
$$- \frac{875 \pi^{10} \left(\operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} + \pi\right) \left(\operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)} + \pi\right) \operatorname{atan}{\left(\frac{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}}{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}} \right)} \operatorname{atan}{\left(\frac{\sqrt{2 - \sqrt{2}} + \sqrt{\sqrt{2} + 2}}{- \sqrt{\sqrt{2} + 2} + \sqrt{2 - \sqrt{2}}} \right)}}{7077888}$$
-875*pi^10*(pi + atan((sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2)))/(sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2)))))*(pi + atan((sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2)))/(sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2)))))*atan((sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2)))/(sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2))))*atan((sqrt(2 + sqrt(2)) + sqrt(2 - sqrt(2)))/(sqrt(2 - sqrt(2)) - sqrt(2 + sqrt(2))))/7077888
Respuesta numérica
[src]
x1 = 67.9369411338793
x2 = -82.0741080750334
x3 = 70.2931356240716
x4 = -3.66519142918809
x5 = 38.2227106186758
x6 = 88.3572933822129
x7 = -61.6537558266997
x8 = 66.3661448070844
x9 = 97.9129710368819
x10 = -9.94837673636768
x11 = -56.025068989018
x12 = 74.2201264410589
x13 = 60.2138591938044
x14 = 5.89048622548086
x15 = 4.31968989868597
x16 = -73.8274273593601
x17 = 8.24668071567321
x18 = 33.3794219443916
x19 = 62.3082542961976
x20 = -100.007366139275
x21 = 22.3838476568273
x22 = 96.2112750161874
x23 = 42.0188017417635
x24 = 71.8639319508665
x25 = 6750.75901378887
x26 = 49.872783375738
x27 = -57.7267650097125
x28 = -78.0162175641465
x29 = 14.1371669411541
x30 = -7.85398163397448
x31 = 45.9457925587507
x32 = 80.1106126665397
x33 = -91.6297857297023
x34 = -38.0918109247762
x35 = 100.007366139275
x36 = -23.9546439836222
x37 = -43.5895980685584
x38 = 52.2289778659303
x39 = -29.845130209103
x40 = -20.0276531666349
x41 = 53.9306738866248
x42 = 26.3108384738145
x43 = -69.6386371545737
x44 = -42.0188017417635
x45 = -75.7909227678538
x46 = -53.7997741927252
x47 = -12.0427718387609
x48 = 82.2050077689329
x49 = -47.6474885794452
x50 = -21.5984494934298
x51 = 9.94837673636768
x52 = 75.9218224617533
x53 = -49.7418836818384
x54 = 23.9546439836222
x55 = 0.392699081698724
x56 = 20.0276531666349
x57 = -95.8185759344887
x58 = -86.0010988920206
x59 = -93.7241808320955
x60 = -13.7444678594553
x61 = -35.7356164345839
x62 = -64.009950316892
x63 = -1.96349540849362
x64 = 58.1194640914112
x65 = -16.1006623496477
x66 = -67.9369411338793
x67 = -71.733032256967
x68 = -87.4409955249159
x69 = 48.3019870489431
x70 = 86.0010988920206
x71 = -83.6449044018282
x72 = 36.1283155162826
x73 = 44.3749962319558
x74 = -39.6626072515711
x75 = 93.8550805259951
x76 = 54.9778714378214
x77 = 78.0162175641465
x78 = 18.3259571459405
x79 = -25.6563400043166
x80 = 31.9395253114962
x81 = 89.9280897090078
x82 = 30.2378292908018
x83 = -79.717913584841
x84 = -5.75958653158129
x85 = -27.7507351067098
x86 = -34.0339204138894
x87 = -17.6714586764426
x88 = -97.7820713429823
x89 = -60.0829594999048
x90 = 84.2994028713261
x91 = 27.8816348006094
x92 = 16.2315620435473
x93 = -45.9457925587507
x94 = -51.8362787842316
x95 = 40.317105721069
x96 = 92.2842841992002
x97 = 1.96349540849362
x98 = -89.9280897090078
x99 = 64.009950316892
x99 = 64.009950316892
Gráfico