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sin^3(x)+sinx+2^0.5=2^0.5*cos2x la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
   3                 ___     ___         
sin (x) + sin(x) + \/ 2  = \/ 2 *cos(2*x)
$$\left(\sin^{3}{\left(x \right)} + \sin{\left(x \right)}\right) + \sqrt{2} = \sqrt{2} \cos{\left(2 x \right)}$$
Gráfica
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
x2 = pi
$$x_{2} = \pi$$
           /                         ____________\
           |  /      ___\     ___   /        ___ |
x3 = -I*log\I*\1 - \/ 2 / - \/ 2 *\/  -1 + \/ 2  /
$$x_{3} = - i \log{\left(- \sqrt{2} \sqrt{-1 + \sqrt{2}} + i \left(1 - \sqrt{2}\right) \right)}$$
           /                         ____________\
           |  /      ___\     ___   /        ___ |
x4 = -I*log\I*\1 - \/ 2 / + \/ 2 *\/  -1 + \/ 2  /
$$x_{4} = - i \log{\left(\sqrt{2} \sqrt{-1 + \sqrt{2}} + i \left(1 - \sqrt{2}\right) \right)}$$
                 /                     ___________\
       pi        |      ___     ___   /       ___ |
x5 = - -- - I*log\1 + \/ 2  + \/ 2 *\/  1 + \/ 2  /
       2                                           
$$x_{5} = - \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} + \sqrt{2} \sqrt{1 + \sqrt{2}} \right)}$$
                 /                     ___________\
       pi        |      ___     ___   /       ___ |
x6 = - -- - I*log\1 + \/ 2  - \/ 2 *\/  1 + \/ 2  /
       2                                           
$$x_{6} = - \frac{\pi}{2} - i \log{\left(- \sqrt{2} \sqrt{1 + \sqrt{2}} + 1 + \sqrt{2} \right)}$$
x6 = -pi/2 - i*log(-sqrt(2)*sqrt(1 + sqrt(2)) + 1 + sqrt(2))
Suma y producto de raíces [src]
suma
          /                         ____________\        /                         ____________\               /                     ___________\               /                     ___________\
          |  /      ___\     ___   /        ___ |        |  /      ___\     ___   /        ___ |     pi        |      ___     ___   /       ___ |     pi        |      ___     ___   /       ___ |
pi - I*log\I*\1 - \/ 2 / - \/ 2 *\/  -1 + \/ 2  / - I*log\I*\1 - \/ 2 / + \/ 2 *\/  -1 + \/ 2  / + - -- - I*log\1 + \/ 2  + \/ 2 *\/  1 + \/ 2  / + - -- - I*log\1 + \/ 2  - \/ 2 *\/  1 + \/ 2  /
                                                                                                     2                                                2                                           
$$\left(\left(- i \log{\left(\sqrt{2} \sqrt{-1 + \sqrt{2}} + i \left(1 - \sqrt{2}\right) \right)} + \left(- i \log{\left(- \sqrt{2} \sqrt{-1 + \sqrt{2}} + i \left(1 - \sqrt{2}\right) \right)} + \pi\right)\right) + \left(- \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} + \sqrt{2} \sqrt{1 + \sqrt{2}} \right)}\right)\right) + \left(- \frac{\pi}{2} - i \log{\left(- \sqrt{2} \sqrt{1 + \sqrt{2}} + 1 + \sqrt{2} \right)}\right)$$
=
       /                         ____________\        /                         ____________\        /                     ___________\        /                     ___________\
       |  /      ___\     ___   /        ___ |        |  /      ___\     ___   /        ___ |        |      ___     ___   /       ___ |        |      ___     ___   /       ___ |
- I*log\I*\1 - \/ 2 / + \/ 2 *\/  -1 + \/ 2  / - I*log\I*\1 - \/ 2 / - \/ 2 *\/  -1 + \/ 2  / - I*log\1 + \/ 2  + \/ 2 *\/  1 + \/ 2  / - I*log\1 + \/ 2  - \/ 2 *\/  1 + \/ 2  /
$$- i \log{\left(- \sqrt{2} \sqrt{-1 + \sqrt{2}} + i \left(1 - \sqrt{2}\right) \right)} - i \log{\left(\sqrt{2} \sqrt{-1 + \sqrt{2}} + i \left(1 - \sqrt{2}\right) \right)} - i \log{\left(1 + \sqrt{2} + \sqrt{2} \sqrt{1 + \sqrt{2}} \right)} - i \log{\left(- \sqrt{2} \sqrt{1 + \sqrt{2}} + 1 + \sqrt{2} \right)}$$
producto
     /      /                         ____________\\ /      /                         ____________\\ /            /                     ___________\\ /            /                     ___________\\
     |      |  /      ___\     ___   /        ___ || |      |  /      ___\     ___   /        ___ || |  pi        |      ___     ___   /       ___ || |  pi        |      ___     ___   /       ___ ||
0*pi*\-I*log\I*\1 - \/ 2 / - \/ 2 *\/  -1 + \/ 2  //*\-I*log\I*\1 - \/ 2 / + \/ 2 *\/  -1 + \/ 2  //*|- -- - I*log\1 + \/ 2  + \/ 2 *\/  1 + \/ 2  /|*|- -- - I*log\1 + \/ 2  - \/ 2 *\/  1 + \/ 2  /|
                                                                                                     \  2                                           / \  2                                           /
$$- i \log{\left(\sqrt{2} \sqrt{-1 + \sqrt{2}} + i \left(1 - \sqrt{2}\right) \right)} 0 \pi \left(- i \log{\left(- \sqrt{2} \sqrt{-1 + \sqrt{2}} + i \left(1 - \sqrt{2}\right) \right)}\right) \left(- \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} + \sqrt{2} \sqrt{1 + \sqrt{2}} \right)}\right) \left(- \frac{\pi}{2} - i \log{\left(- \sqrt{2} \sqrt{1 + \sqrt{2}} + 1 + \sqrt{2} \right)}\right)$$
=
0
$$0$$
0
Respuesta numérica [src]
x1 = 65.9734457253857
x2 = 69.1150383789755
x3 = -21.9911485751286
x4 = 21.9911485751286
x5 = -3.14159265358979
x6 = -15.707963267949
x7 = 172.787595947439
x8 = 3.56867123998227
x9 = 6.28318530717959
x10 = -59.2631818318136
x11 = -71.8295524461728
x12 = 16.1350418543414
x13 = 28.2743338823081
x14 = -94.2477796076938
x15 = -12.9934492007516
x16 = -12.5663706143592
x17 = -53.4070751110265
x18 = 84.8230016469244
x19 = -31.8430051222904
x20 = -128.378220210789
x21 = 30.9888479495055
x22 = 62.4047744854034
x23 = 100.103886328481
x24 = 25.1327412287183
x25 = 72.2566310325652
x26 = 47.5509683902394
x27 = -25.5598198151108
x28 = -50.2654824574367
x29 = 72.6837096189577
x30 = 78.5398163397448
x31 = -87.9645943005142
x32 = 37.6991118430775
x33 = -6.28318530717959
x34 = -37.6991118430775
x35 = -43.9822971502571
x36 = 68.687959792583
x37 = 47.1238898038469
x38 = -84.3959230605319
x39 = -63.2589316581883
x40 = -100.530964914873
x41 = 3.14159265358979
x42 = -78.1127377533523
x43 = -81.6814089933346
x44 = -19.2766345079312
x45 = -46.6968112174544
x46 = -40.8407044966673
x47 = -65.9734457253857
x48 = 0.0
x49 = 12.1392920279667
x50 = -56.5486677646163
x51 = 91.106186954104
x52 = 31.4159265358979
x53 = 56.1215891782238
x54 = 24.7056626423259
x55 = 43.9822971502571
x56 = -47.1238898038469
x57 = 213.201221857713
x58 = 97.8164508476761
x59 = -97.3893722612836
x60 = 81.6814089933346
x61 = 298.878380677423
x62 = -69.5421169653679
x63 = 50.2654824574367
x64 = 94.2477796076938
x65 = 53.834153697419
x66 = -84.8230016469244
x67 = -91.106186954104
x68 = -40.4136259102748
x69 = -59.6902604182061
x70 = -34.1304406030953
x71 = -75.8253022725475
x72 = 18.4224773351463
x73 = 34.5575191894877
x74 = 60.1173390045985
x75 = -62.8318530717959
x76 = 148.081933305113
x77 = -18.8495559215388
x78 = 87.9645943005142
x79 = -27.8472552959157
x80 = 40.8407044966673
x81 = -9.42477796076938
x82 = 91.5332655404965
x83 = 9.85185654716186
x84 = -31.4159265358979
x85 = 75.398223686155
x85 = 75.398223686155