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4sin^3(x)+3sin(x)+2*sqrt(3)=2*sqrt(3)cos(2x) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
     3                     ___       ___         
4*sin (x) + 3*sin(x) + 2*\/ 3  = 2*\/ 3 *cos(2*x)
$$\left(4 \sin^{3}{\left(x \right)} + 3 \sin{\left(x \right)}\right) + 2 \sqrt{3} = 2 \sqrt{3} \cos{\left(2 x \right)}$$
Gráfica
Suma y producto de raíces [src]
suma
  2*pi   pi     
- ---- - -- + pi
   3     3      
$$\left(- \frac{2 \pi}{3} - \frac{\pi}{3}\right) + \pi$$
=
0
$$0$$
producto
  -2*pi -pi    
0*-----*----*pi
    3    3     
$$\pi - \frac{\pi}{3} \cdot 0 \left(- \frac{2 \pi}{3}\right)$$
=
0
$$0$$
0
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     -2*pi
x2 = -----
       3  
$$x_{2} = - \frac{2 \pi}{3}$$
     -pi 
x3 = ----
      3  
$$x_{3} = - \frac{\pi}{3}$$
x4 = pi
$$x_{4} = \pi$$
x4 = pi
Respuesta numérica [src]
x1 = 65.9734457253857
x2 = 74.3510260865825
x3 = 54.4542725277176
x4 = 69.1150383789755
x5 = -21.9911485751286
x6 = 21.9911485751286
x7 = 68.0678406963184
x8 = -3.14159265358979
x9 = -15.707963267949
x10 = 97.3893722612836
x11 = -90.0589893597647
x12 = 61.7846553140444
x13 = -33.5103221961608
x14 = 6.28318530717959
x15 = -71.2094333154912
x16 = -26.1799386344983
x17 = -2.09439504775496
x18 = 28.2743338823081
x19 = -94.2477796076938
x20 = -12.5663706143592
x21 = -76.445421069921
x22 = -57.5958653719793
x23 = 41.887902105778
x24 = -83.7758043512187
x25 = -25.1327412287183
x26 = -53.4070751110265
x27 = 16.7551607882915
x28 = 84.8230016469244
x29 = -77.4926192916478
x30 = -27.2271362706148
x31 = -77.4926189506521
x32 = 10.4719753677172
x33 = 4.18879025418915
x34 = 25.1327412287183
x35 = 72.2566310325652
x36 = -50.2654824574367
x37 = 55.5014702703265
x38 = 92.153384589409
x39 = 78.5398163397448
x40 = -87.9645943005142
x41 = 37.6991118430775
x42 = -6.28318530717959
x43 = -37.6991118430775
x44 = -43.9822971502571
x45 = 47.1238898038469
x46 = -13.6135682206187
x47 = 48.171087421204
x48 = 30.3687289323009
x49 = -95.2949772983652
x50 = -100.530964914873
x51 = 3.14159265358979
x52 = -83.7758040760293
x53 = -46.0766922028656
x54 = -81.6814089933346
x55 = 55.5014699570785
x56 = -40.8407044966673
x57 = -65.9734457253857
x58 = 0.0
x59 = -46.0766921447527
x60 = 99.4837673412439
x61 = 10.4719752740545
x62 = -56.5486677646163
x63 = 98.4365696881637
x64 = 91.106186954104
x65 = 31.4159265358979
x66 = 43.9822971502571
x67 = -47.1238898038469
x68 = -97.3893722612836
x69 = 60.7374578772492
x70 = 17.8023585258693
x71 = 81.6814089933346
x72 = 50.2654824574367
x73 = 94.2477796076938
x74 = -84.8230016469244
x75 = -91.106186954104
x76 = -59.6902604182061
x77 = -33.5103217917668
x78 = -69.1150383789755
x79 = 24.0855436595079
x80 = -32.4631239430029
x81 = 85.8701992578193
x82 = -39.7935069114296
x83 = 34.5575191894877
x84 = -62.8318530717959
x85 = -70.1622357955183
x86 = 11.5191731725327
x87 = -18.8495559215388
x88 = 80.6342111930818
x89 = 87.9645943005142
x90 = 40.8407044966673
x91 = -9.42477796076938
x92 = 11.5191726923297
x93 = 61.7846556855441
x94 = 75.398223686155
x94 = 75.398223686155