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- La ecuación:
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Ecuación x^3-x^2-x-1=0
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Ecuación 0,2x+2,7=1,4-1,1x
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Ecuación x^2=2x+8
- Expresar {x} en función de y en la ecuación:
- -11*x-14*y=-3
- -9*x-1*y=6
- -2*x+2*y=4
- -11*x-3*y=14
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Expresiones idénticas
- tres *(cos(x))^ dos - tres *(sin(x))^ dos - uno -cos(x)-sin(x)= cero
- 3 multiplicar por ( coseno de (x)) al cuadrado menos 3 multiplicar por ( seno de (x)) al cuadrado menos 1 menos coseno de (x) menos seno de (x) es igual a 0
- tres multiplicar por ( coseno de (x)) en el grado dos menos tres multiplicar por ( seno de (x)) en el grado dos menos uno menos coseno de (x) menos seno de (x) es igual a cero
- 3*(cos(x))2-3*(sin(x))2-1-cos(x)-sin(x)=0
- 3*cosx2-3*sinx2-1-cosx-sinx=0
- 3*(cos(x))²-3*(sin(x))²-1-cos(x)-sin(x)=0
- 3*(cos(x)) en el grado 2-3*(sin(x)) en el grado 2-1-cos(x)-sin(x)=0
- 3(cos(x))^2-3(sin(x))^2-1-cos(x)-sin(x)=0
- 3(cos(x))2-3(sin(x))2-1-cos(x)-sin(x)=0
- 3cosx2-3sinx2-1-cosx-sinx=0
- 3cosx^2-3sinx^2-1-cosx-sinx=0
- 3*(cos(x))^2-3*(sin(x))^2-1-cos(x)-sin(x)=O
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Expresiones semejantes
- 3*(cos(x))^2-3*(sin(x))^2-1+cos(x)-sin(x)=0
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Expresiones con funciones
- Coseno cos
- cos(x)=-3
- cos(0.5-y)-0.5y+2=0
- cos(7*x)+cos(x)=0
- cos(2*x-pi/4)=0
- cos(x)=-(2/5)
- Seno sin
- sin(x)=1/3
- sin(6*x)=9/8
- sin(2x)=-1/2
- sin(3*x)-cos(3*x)=0
- sin(x)^(2)-sin(x)=0
- Coseno cos
- cos(x)=-3
- cos(0.5-y)-0.5y+2=0
- cos(7*x)+cos(x)=0
- cos(2*x-pi/4)=0
- cos(x)=-(2/5)
- Seno sin
- sin(x)=1/3
- sin(6*x)=9/8
- sin(2x)=-1/2
- sin(3*x)-cos(3*x)=0
- sin(x)^(2)-sin(x)=0
3*(cos(x))^2-3*(sin(x))^2-1-cos(x)-sin(x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 3*cos (x) - 3*sin (x) - 1 - cos(x) - sin(x) = 0
$$\left(\left(\left(- 3 \sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)}\right) - 1\right) - \cos{\left(x \right)}\right) - \sin{\left(x \right)} = 0$$
Respuesta rápida
[src]
/ ___________________________________________________________________________________________________________________________________________________________ \
| / ______________________ 3 ___ 5/6 |
| 5/12 / 6 ___ ___ 3 / _______ 79*\/ 2 53*2 |
| 2 * / 41*\/ 2 - \/ 2 *\/ -329 + 3*I*\/ 21057 - -------------------------------------------------------------------------------- - ------------------------- |
| / _________________________________________________________________________ ______________________ _________________________________________________________________________|
| / / ______________________ 3 / _______ / ______________________ |
| / / 3 ___ 212 2/3 3 / _______ \/ -329 + 3*I*\/ 21057 5/6 / 3 ___ 212 2/3 3 / _______ |
| / / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 2 * / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 |
| / / ______________________ / ______________________ |
| / / 3 / _______ / 3 / _______ |
| 1 \/ \/ \/ -329 + 3*I*\/ 21057 \/ \/ -329 + 3*I*\/ 21057 |
x1 = -2*atan|- - + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------|
\ 6 6 12 /
$$x_{1} = - 2 \operatorname{atan}{\left(- \frac{1}{6} + \frac{2^{\frac{5}{12}} \sqrt{41 \sqrt[6]{2} - \sqrt{2} \sqrt[3]{-329 + 3 \sqrt{21057} i} - \frac{79 \sqrt[3]{2}}{\sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}} - \frac{53 \cdot 2^{\frac{5}{6}}}{\sqrt[3]{-329 + 3 \sqrt{21057} i}}}}{6} + \frac{2^{\frac{5}{6}} \sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}}{12} \right)}$$
/ / ___________________________________________________________________________________________________________________________________________________________ \\ / / ___________________________________________________________________________________________________________________________________________________________ \\
| | / ______________________ 5/6 3 ___ || | | / ______________________ 5/6 3 ___ ||
| | 5/12 / 6 ___ ___ 3 / _______ 53*2 79*\/ 2 || | | 5/12 / 6 ___ ___ 3 / _______ 53*2 79*\/ 2 ||
| | 2 * / 41*\/ 2 - \/ 2 *\/ -329 + 3*I*\/ 21057 - ------------------------- + -------------------------------------------------------------------------------- || | | 2 * / 41*\/ 2 - \/ 2 *\/ -329 + 3*I*\/ 21057 - ------------------------- + -------------------------------------------------------------------------------- ||
| | / ______________________ _________________________________________________________________________ _________________________________________________________________________|| | | / ______________________ _________________________________________________________________________ _________________________________________________________________________||
| | / 3 / _______ / ______________________ / ______________________ || | | / 3 / _______ / ______________________ / ______________________ ||
| | / \/ -329 + 3*I*\/ 21057 / 3 ___ 212 2/3 3 / _______ 5/6 / 3 ___ 212 2/3 3 / _______ || | | / \/ -329 + 3*I*\/ 21057 / 3 ___ 212 2/3 3 / _______ 5/6 / 3 ___ 212 2/3 3 / _______ ||
| | / / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 2 * / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 || | | / / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 2 * / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 ||
| | / / ______________________ / ______________________ || | | / / ______________________ / ______________________ ||
| | / / 3 / _______ / 3 / _______ || | | / / 3 / _______ / 3 / _______ ||
| |1 \/ \/ \/ -329 + 3*I*\/ 21057 \/ \/ -329 + 3*I*\/ 21057 || | |1 \/ \/ \/ -329 + 3*I*\/ 21057 \/ \/ -329 + 3*I*\/ 21057 ||
x2 = 2*re|atan|- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------|| + 2*I*im|atan|- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------||
\ \6 6 12 // \ \6 6 12 //
$$x_{2} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{2^{\frac{5}{12}} \sqrt{41 \sqrt[6]{2} - \sqrt{2} \sqrt[3]{-329 + 3 \sqrt{21057} i} + \frac{79 \sqrt[3]{2}}{\sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}} - \frac{53 \cdot 2^{\frac{5}{6}}}{\sqrt[3]{-329 + 3 \sqrt{21057} i}}}}{6} + \frac{2^{\frac{5}{6}} \sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}}{12} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{2^{\frac{5}{12}} \sqrt{41 \sqrt[6]{2} - \sqrt{2} \sqrt[3]{-329 + 3 \sqrt{21057} i} + \frac{79 \sqrt[3]{2}}{\sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}} - \frac{53 \cdot 2^{\frac{5}{6}}}{\sqrt[3]{-329 + 3 \sqrt{21057} i}}}}{6} + \frac{2^{\frac{5}{6}} \sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}}{12} \right)}\right)}$$
/ ___________________________________________________________________________________________________________________________________________________________ \
| / ______________________ 5/6 3 ___ |
| 5/12 / 6 ___ ___ 3 / _______ 53*2 79*\/ 2 |
| 2 * / 41*\/ 2 - \/ 2 *\/ -329 + 3*I*\/ 21057 - ------------------------- + -------------------------------------------------------------------------------- |
| / ______________________ _________________________________________________________________________ _________________________________________________________________________|
| / 3 / _______ / ______________________ / ______________________ |
| / \/ -329 + 3*I*\/ 21057 / 3 ___ 212 2/3 3 / _______ 5/6 / 3 ___ 212 2/3 3 / _______ |
| / / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 2 * / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 |
| / / ______________________ / ______________________ |
| / / 3 / _______ / 3 / _______ |
|1 \/ \/ \/ -329 + 3*I*\/ 21057 \/ \/ -329 + 3*I*\/ 21057 |
x3 = 2*atan|- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------|
\6 6 12 /
$$x_{3} = 2 \operatorname{atan}{\left(\frac{1}{6} + \frac{2^{\frac{5}{12}} \sqrt{41 \sqrt[6]{2} - \sqrt{2} \sqrt[3]{-329 + 3 \sqrt{21057} i} + \frac{79 \sqrt[3]{2}}{\sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}} - \frac{53 \cdot 2^{\frac{5}{6}}}{\sqrt[3]{-329 + 3 \sqrt{21057} i}}}}{6} + \frac{2^{\frac{5}{6}} \sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}}{12} \right)}$$
/ / ___________________________________________________________________________________________________________________________________________________________\\ / / ___________________________________________________________________________________________________________________________________________________________\\
| | / ______________________ 3 ___ 5/6 || | | / ______________________ 3 ___ 5/6 ||
| | 5/12 / 6 ___ ___ 3 / _______ 79*\/ 2 53*2 || | | 5/12 / 6 ___ ___ 3 / _______ 79*\/ 2 53*2 ||
| | 2 * / 41*\/ 2 - \/ 2 *\/ -329 + 3*I*\/ 21057 - -------------------------------------------------------------------------------- - ------------------------- || | | 2 * / 41*\/ 2 - \/ 2 *\/ -329 + 3*I*\/ 21057 - -------------------------------------------------------------------------------- - ------------------------- ||
| | _________________________________________________________________________ / _________________________________________________________________________ ______________________ || | | _________________________________________________________________________ / _________________________________________________________________________ ______________________ ||
| | / ______________________ / / ______________________ 3 / _______ || | | / ______________________ / / ______________________ 3 / _______ ||
| | 5/6 / 3 ___ 212 2/3 3 / _______ / / 3 ___ 212 2/3 3 / _______ \/ -329 + 3*I*\/ 21057 || | | 5/6 / 3 ___ 212 2/3 3 / _______ / / 3 ___ 212 2/3 3 / _______ \/ -329 + 3*I*\/ 21057 ||
| | 2 * / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 / / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 || | | 2 * / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 / / 41*\/ 2 + ------------------------- + 2*2 *\/ -329 + 3*I*\/ 21057 ||
| | / ______________________ / / ______________________ || | | / ______________________ / / ______________________ ||
| | / 3 / _______ / / 3 / _______ || | | / 3 / _______ / / 3 / _______ ||
| |1 \/ \/ -329 + 3*I*\/ 21057 \/ \/ \/ -329 + 3*I*\/ 21057 || | |1 \/ \/ -329 + 3*I*\/ 21057 \/ \/ \/ -329 + 3*I*\/ 21057 ||
x4 = 2*re|atan|- - ------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| + 2*I*im|atan|- - ------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------||
\ \6 12 6 // \ \6 12 6 //
$$x_{4} = 2 \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{2^{\frac{5}{6}} \sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}}{12} + \frac{2^{\frac{5}{12}} \sqrt{41 \sqrt[6]{2} - \sqrt{2} \sqrt[3]{-329 + 3 \sqrt{21057} i} - \frac{79 \sqrt[3]{2}}{\sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}} - \frac{53 \cdot 2^{\frac{5}{6}}}{\sqrt[3]{-329 + 3 \sqrt{21057} i}}}}{6} \right)}\right)} + 2 i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{6} - \frac{2^{\frac{5}{6}} \sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}}{12} + \frac{2^{\frac{5}{12}} \sqrt{41 \sqrt[6]{2} - \sqrt{2} \sqrt[3]{-329 + 3 \sqrt{21057} i} - \frac{79 \sqrt[3]{2}}{\sqrt{41 \sqrt[3]{2} + \frac{212}{\sqrt[3]{-329 + 3 \sqrt{21057} i}} + 2 \cdot 2^{\frac{2}{3}} \sqrt[3]{-329 + 3 \sqrt{21057} i}}} - \frac{53 \cdot 2^{\frac{5}{6}}}{\sqrt[3]{-329 + 3 \sqrt{21057} i}}}}{6} \right)}\right)}$$
x4 = 2*re(atan(1/6 - 2^(5/6)*sqrt(41*2^(1/3) + 212/(-329 + 3*sqrt(21057)*i)^(1/3) + 2*2^(2/3)*(-329 + 3*sqrt(21057)*i)^(1/3))/12 + 2^(5/12)*sqrt(41*2^(1/6) - sqrt(2)*(-329 + 3*sqrt(21057)*i)^(1/3) - 79*2^(1/3)/sqrt(41*2^(1/3) + 212/(-329 + 3*sqrt(21057)*i)^(1/3) + 2*2^(2/3)*(-329 + 3*sqrt(21057)*i)^(1/3)) - 53*2^(5/6)/(-329 + 3*sqrt(21057)*i)^(1/3))/6)) + 2*i*im(atan(1/6 - 2^(5/6)*sqrt(41*2^(1/3) + 212/(-329 + 3*sqrt(21057)*i)^(1/3) + 2*2^(2/3)*(-329 + 3*sqrt(21057)*i)^(1/3))/12 + 2^(5/12)*sqrt(41*2^(1/6) - sqrt(2)*(-329 + 3*sqrt(21057)*i)^(1/3) - 79*2^(1/3)/sqrt(41*2^(1/3) + 212/(-329 + 3*sqrt(21057)*i)^(1/3) + 2*2^(2/3)*(-329 + 3*sqrt(21057)*i)^(1/3)) - 53*2^(5/6)/(-329 + 3*sqrt(21057)*i)^(1/3))/6))
Respuesta numérica
[src]
x1 = -38.2568657863132
x2 = -145.071016008366
x3 = 75.750963948744
x4 = -43.6295568876681
x5 = -33.7034254467166
x6 = 16.5620570107201
x7 = 71.6075509704407
x8 = -77.6857225969737
x9 = -3.7906727157143
x10 = 96.7402921991591
x11 = 0.352740262588992
x12 = -83.9689079041533
x13 = 88.3173345631032
x14 = 41.6947982394385
x15 = 18.2918019783031
x16 = -54.056155173151
x17 = 19.2022961841277
x18 = -5.93044504459059
x19 = 50.6182227200257
x20 = 47.9779835466181
x21 = -87.6118540379252
x22 = -100.178224652284
x23 = 85.6770953896956
x24 = 54.2611688537976
x25 = 25.4854814913073
x26 = 77.8907362776203
x27 = 5.72543136394394
x28 = 10.2788717035405
x29 = 98.2434660040548
x30 = -16.3570433300735
x31 = -25.690495171954
x32 = -10.0738580228939
x33 = 91.9602806968752
x34 = -27.420240139537
x35 = -63.3896070150315
x36 = -93.8950393451048
x37 = -245.60198092324
x38 = -12.2136303517702
x39 = -163.920571929905
x40 = 82.0341492559236
x41 = -41.4897845587918
x42 = 190.988071806853
x43 = 46.4748097417224
x44 = 44.3350374128461
x45 = -31.9736804791336
x46 = -62.4791128092069
x47 = -24.7800009661294
x48 = -90.2520932113328
x49 = 2.49251259146528
x50 = -85.4720817090489
x51 = -35.2065992516122
x52 = -49.9127421948477
x53 = 90.4571068919795
x54 = 52.757995048902
x55 = 31.7686667984869
x56 = 8.77569789864487
x57 = -2.28749891081863
x58 = -60.3393404803306
x59 = 3.99568639636095
x60 = -91.7552670162285
x61 = 68.5572844357398
x62 = 24.5749872854827
x63 = 33.9084391273632
x64 = -39.9866107538962
x65 = -47.7729698659714
x66 = -18.4968156589498
x67 = -71.4025372897941
x68 = 62.2740991285602
x69 = 99.9732109716377
x70 = -79.1888964018693
x71 = -19.4073098647744
x72 = -98.0384523234081
x73 = 69.4677786415645
x74 = -94.8055335509294
x75 = 55.9909138213806
x76 = 12.0086166711235
x77 = 27.6252538201836
x78 = -56.1959275020273
x79 = 38.0518521056665
x80 = -69.6727923222111
x81 = -82.2391629365703
x82 = -31.0631862733089
x83 = 40.1916244345428
x84 = -8.57068421799822
x85 = 60.5443541609772
x86 = 84.1739215847999
x87 = -75.9559776293907
x88 = -46.2697960610757
x88 = -46.2697960610757