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tgx-1/3×tg^3x-1/5×tg^5x=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
            3         5       
         tan (x)   tan (x)    
tan(x) - ------- - ------- = 0
            3         5
$$\left(- \frac{\tan^{3}{\left(x \right)}}{3} + \tan{\left(x \right)}\right) - \frac{\tan^{5}{\left(x \right)}}{5} = 0$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
x1 = 0
$$x_{1} = 0$$ 
           /     /     _____________\\     /     /     _____________\\
           |     |    /       _____ ||     |     |    /       _____ ||
           |     |   /  5   \/ 205  ||     |     |   /  5   \/ 205  ||
x2 = - I*re|atanh|  /   - + ------- || + im|atanh|  /   - + ------- ||
           \     \\/    6      6    //     \     \\/    6      6    //
$$x_{2} = \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)} - i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)}$$ 
         /     /     _____________\\       /     /     _____________\\
         |     |    /       _____ ||       |     |    /       _____ ||
         |     |   /  5   \/ 205  ||       |     |   /  5   \/ 205  ||
x3 = - im|atanh|  /   - + ------- || + I*re|atanh|  /   - + ------- ||
         \     \\/    6      6    //       \     \\/    6      6    //
$$x_{3} = - \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)} + i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)}$$ 
          /     _______________\
          |    /         _____ |
          |   /    5   \/ 205  |
x4 = -atan|  /   - - + ------- |
          \\/      6      6    /
$$x_{4} = - \operatorname{atan}{\left(\sqrt{- \frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}$$ 
         /     _______________\
         |    /         _____ |
         |   /    5   \/ 205  |
x5 = atan|  /   - - + ------- |
         \\/      6      6    /
$$x_{5} = \operatorname{atan}{\left(\sqrt{- \frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}$$ 
x5 = atan(sqrt(-5/6 + sqrt(205)/6))
Suma y producto de raíces [src] 
suma
      /     /     _____________\\     /     /     _____________\\       /     /     _____________\\       /     /     _____________\\       /     _______________\       /     _______________\
      |     |    /       _____ ||     |     |    /       _____ ||       |     |    /       _____ ||       |     |    /       _____ ||       |    /         _____ |       |    /         _____ |
      |     |   /  5   \/ 205  ||     |     |   /  5   \/ 205  ||       |     |   /  5   \/ 205  ||       |     |   /  5   \/ 205  ||       |   /    5   \/ 205  |       |   /    5   \/ 205  |
- I*re|atanh|  /   - + ------- || + im|atanh|  /   - + ------- || + - im|atanh|  /   - + ------- || + I*re|atanh|  /   - + ------- || - atan|  /   - - + ------- | + atan|  /   - - + ------- |
      \     \\/    6      6    //     \     \\/    6      6    //       \     \\/    6      6    //       \     \\/    6      6    //       \\/      6      6    /       \\/      6      6    /
$$\operatorname{atan}{\left(\sqrt{- \frac{5}{6} + \frac{\sqrt{205}}{6}} \right)} + \left(- \operatorname{atan}{\left(\sqrt{- \frac{5}{6} + \frac{\sqrt{205}}{6}} \right)} + \left(\left(\operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)} - i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)}\right) + \left(- \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)} + i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)}\right)\right)\right)$$ 
=
0
$$0$$ 
producto
  /      /     /     _____________\\     /     /     _____________\\\ /    /     /     _____________\\       /     /     _____________\\\ /     /     _______________\\     /     _______________\
  |      |     |    /       _____ ||     |     |    /       _____ ||| |    |     |    /       _____ ||       |     |    /       _____ ||| |     |    /         _____ ||     |    /         _____ |
  |      |     |   /  5   \/ 205  ||     |     |   /  5   \/ 205  ||| |    |     |   /  5   \/ 205  ||       |     |   /  5   \/ 205  ||| |     |   /    5   \/ 205  ||     |   /    5   \/ 205  |
0*|- I*re|atanh|  /   - + ------- || + im|atanh|  /   - + ------- |||*|- im|atanh|  /   - + ------- || + I*re|atanh|  /   - + ------- |||*|-atan|  /   - - + ------- ||*atan|  /   - - + ------- |
  \      \     \\/    6      6    //     \     \\/    6      6    /// \    \     \\/    6      6    //       \     \\/    6      6    /// \     \\/      6      6    //     \\/      6      6    /
$$\left(- \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)} + i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)}\right) 0 \left(\operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)} - i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{\frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right)}\right) \left(- \operatorname{atan}{\left(\sqrt{- \frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}\right) \operatorname{atan}{\left(\sqrt{- \frac{5}{6} + \frac{\sqrt{205}}{6}} \right)}$$ 
=
0
$$0$$ 
0
Respuesta numérica [src] 
x1 = 62.8318530717959
x2 = -50.2654824574367
x3 = -30.5213637872484
x4 = 19.7441186701883
x5 = -17.9549931728892
x6 = -13.4609333630087
x7 = 72.2566310325652
x8 = 96.494809512634
x9 = -43.9822971502571
x10 = 2.24702990494023
x11 = 32.3104892845475
x12 = -37.6991118430775
x13 = 34.5575191894877
x14 = -94.2477796076938
x15 = -70.009601127625
x16 = 52.5125123623769
x17 = -61.9372903231463
x18 = -56.5486677646163
x19 = -21.9911485751286
x20 = -26.0273039773679
x21 = -15.707963267949
x22 = 50.2654824574367
x23 = -92.0007497027536
x24 = -96.494809512634
x25 = 36.804549094428
x26 = 21.9911485751286
x27 = -87.9645943005142
x28 = 85.717564395574
x29 = -72.2566310325652
x30 = -35.4520819381373
x31 = -2.24702990494023
x32 = -39.9461417480177
x33 = 59.6902604182061
x34 = 84.8230016469244
x35 = -8.53021521211981
x36 = -74.5036609375055
x37 = -9.42477796076938
x38 = -90.2116242054544
x39 = -33.6629564408382
x40 = -79.4343790883944
x41 = -48.0184525524965
x42 = -19.7441186701883
x43 = -65.9734457253857
x44 = 15.707963267949
x45 = -83.9284388982748
x46 = 28.2743338823081
x47 = 94.2477796076938
x48 = 90.2116242054544
x49 = 37.6991118430775
x50 = -4.03615540223936
x51 = 6.28318530717959
x52 = 63.7264158204454
x53 = 70.009601127625
x54 = -57.4432305132658
x55 = 58.7956976695565
x56 = 30.5213637872484
x57 = -53.4070751110265
x58 = 24.2381784800688
x59 = 76.2927864348046
x60 = 92.0007497027536
x61 = -6.28318530717959
x62 = -75.398223686155
x63 = -11.6718078657096
x64 = 14.8134005192994
x65 = -24.2381784800688
x66 = 0.0
x67 = 54.301637859676
x68 = 8.53021521211981
x69 = -97.3893722612836
x70 = -28.2743338823081
x71 = 81.6814089933346
x72 = 100.530964914873
x73 = 41.7352672453169
x74 = -46.2293270551973
x75 = -68.2204756303259
x76 = 78.5398163397448
x77 = -85.717564395574
x78 = 4.03615540223936
x79 = -41.7352672453169
x80 = 26.0273039773679
x81 = 12.5663706143592
x82 = 87.9645943005142
x83 = -63.7264158204454
x84 = 48.0184525524965
x85 = 80.7868462446851
x86 = 43.9822971502571
x87 = -31.4159265358979
x88 = -81.6814089933346
x89 = 56.5486677646163
x90 = 46.2293270551973
x91 = 98.2839350099332
x92 = 74.5036609375055
x93 = 21.096585826479
x94 = -59.6902604182061
x95 = 10.3193407094189
x96 = 68.2204756303259
x97 = 65.9734457253857
x98 = -99.6364021662238
x99 = -52.5125123623769
x99 = -52.5125123623769
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