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sin(2x)+sqrt(2cos(x)-2(cos(x))^3)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
              ______________________    
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sin(2*x) + \/  2*cos(x) - 2*cos (x)  = 0
$$\sqrt{- 2 \cos^{3}{\left(x \right)} + 2 \cos{\left(x \right)}} + \sin{\left(2 x \right)} = 0$$
Gráfica
Suma y producto de raíces [src]
suma
  pi   pi   pi     
- -- - -- + -- + pi
  2    3    2      
$$\left(\left(- \frac{\pi}{2} - \frac{\pi}{3}\right) + \frac{\pi}{2}\right) + \pi$$
=
2*pi
----
 3  
$$\frac{2 \pi}{3}$$
producto
  -pi  -pi  pi   
0*----*----*--*pi
   2    3   2    
$$\pi \frac{\pi}{2} \cdot - \frac{\pi}{3} \cdot 0 \left(- \frac{\pi}{2}\right)$$
=
0
$$0$$
0
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     -pi 
x2 = ----
      2  
$$x_{2} = - \frac{\pi}{2}$$
     -pi 
x3 = ----
      3  
$$x_{3} = - \frac{\pi}{3}$$
     pi
x4 = --
     2 
$$x_{4} = \frac{\pi}{2}$$
x5 = pi
$$x_{5} = \pi$$
x5 = pi
Respuesta numérica [src]
x1 = 49.2182849062401
x2 = -9.42477796076938
x3 = 84.8230016469244
x4 = 21.9911485751286
x5 = -43.9822971502571
x6 = -15.707963267949
x7 = 86.9173967493176
x8 = -91.106186954104 - 3.6618514718342e-19*i
x9 = 53.4070751110265
x10 = 56.5486677646163
x11 = 100.530964914873
x12 = 65.9734457253857
x13 = -51.3126800086333
x14 = -63.8790506229925
x15 = 36.6519142918809
x16 = -37.6991118430775
x17 = -21.9911485751286
x18 = -45.0294947014537
x19 = -82.7286065445312
x20 = -47.1238898038469
x21 = 30.3687289847013
x22 = 40.8407044966673 - 1.40573253628758e-18*i
x23 = 72.2566310325652
x24 = 17.8023583703422
x25 = 12.5663706143592
x26 = -19.8967534727354
x27 = 24.0855436775217
x28 = -13.6135681655558
x29 = -6.28318530717959
x30 = 81.6814089933346
x31 = 15.707963267949
x32 = -34.5575191894877
x33 = 78.5398163397448
x34 = 97.3893722612836 - 9.63597362415685e-19*i
x35 = 80.634211442138
x36 = 5.23598775598299
x37 = 93.2005820564972
x38 = -101.57816246607
x39 = 42.9350995990605
x40 = -78.5398163397448
x41 = 37.6991118430775
x42 = -59.6902604182061
x43 = -50.2654824574367
x44 = -94.2477796076938
x45 = -26.1799387799149
x46 = 34.5575191894877
x47 = -89.0117918517108
x48 = -28.2743338823081
x49 = -57.5958653158129
x50 = -38.7463093942741
x51 = -72.2566310325652
x52 = -53.4070751110265
x53 = -87.9645943005142
x54 = 61.7846555205993
x55 = 59.6902604182061
x56 = -65.9734457253857
x57 = -70.162235930172
x58 = 6.28318530717959
x59 = 0.0
x60 = 87.9645943005142
x61 = -97.3893722612836
x62 = 43.9822971502571
x63 = -7.33038285837618
x64 = -95.2949771588904
x65 = -1.0471975511966
x66 = -75.398223686155
x67 = -31.4159265358979
x68 = 94.2477796076938
x69 = 28.2743338823081
x70 = 68.0678408277789
x71 = 9.42477796076938 - 1.55480920824794e-19*i
x72 = -81.6814089933346
x73 = -3.14159265358979 - 1.23505083309362e-18*i
x74 = 74.3510261349584
x75 = 50.2654824574367
x75 = 50.2654824574367