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(cos2x+cosx+1)/(2sinx+sqrt(3))=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
cos(2*x) + cos(x) + 1    
--------------------- = 0
                ___      
   2*sin(x) + \/ 3       
$$\frac{\left(\cos{\left(x \right)} + \cos{\left(2 x \right)}\right) + 1}{2 \sin{\left(x \right)} + \sqrt{3}} = 0$$
Gráfica
Respuesta rápida [src]
     -pi 
x1 = ----
      2  
$$x_{1} = - \frac{\pi}{2}$$
     pi
x2 = --
     2 
$$x_{2} = \frac{\pi}{2}$$
     2*pi
x3 = ----
      3  
$$x_{3} = \frac{2 \pi}{3}$$
x3 = 2*pi/3
Suma y producto de raíces [src]
suma
  pi   pi   2*pi
- -- + -- + ----
  2    2     3  
$$\left(- \frac{\pi}{2} + \frac{\pi}{2}\right) + \frac{2 \pi}{3}$$
=
2*pi
----
 3  
$$\frac{2 \pi}{3}$$
producto
-pi  pi 2*pi
----*--*----
 2   2   3  
$$\frac{2 \pi}{3} \cdot - \frac{\pi}{2} \frac{\pi}{2}$$
=
   3 
-pi  
-----
  6  
$$- \frac{\pi^{3}}{6}$$
-pi^3/6
Respuesta numérica [src]
x1 = 51.8362787842316
x2 = -36.1283155162826
x3 = 875.457152800356
x4 = -67.0206432765823
x5 = 89.5353906273091
x6 = -35.6047167406843
x7 = 71.2094334813686
x8 = 36.1283155162826
x9 = -4.71238898038469
x10 = 96.342174710087
x11 = -10.471975511966
x12 = -48.1710873550435
x13 = 2.0943951023932
x14 = -41.8879020478639
x15 = -42.4115008234622
x16 = -85.870199198121
x17 = -4.18879020478639
x18 = 77.4926187885482
x19 = -80.1106126665397
x20 = 7.85398163397448
x21 = 39.2699081698724
x22 = -29.845130209103
x23 = 52.3598775598299
x24 = 76.9690200129499
x25 = -23.5619449019235
x26 = 39.7935069454707
x27 = -92.1533845053006
x28 = -17.2787595947439
x29 = 33.5103216382911
x30 = 14.1371669411541
x31 = -54.4542726622231
x32 = 58.1194640914112
x33 = -51.8362787842316
x34 = 80.1106126665397
x35 = 20.943951023932
x36 = -92.6769832808989
x37 = -23.0383461263252
x38 = -60.7374579694027
x39 = 64.4026493985908
x40 = 8.37758040957278
x41 = -98.9601685880785
x42 = -16.7551608191456
x43 = -58.1194640914112
x44 = 86.3937979737193
x45 = -54.9778714378214
x46 = -601.614993162445
x47 = -14.1371669411541
x48 = -48.6946861306418
x49 = 26.7035375555132
x50 = -61.261056745001
x51 = 46.0766922526503
x52 = -7.85398163397448
x53 = 45.553093477052
x54 = -79.5870138909414
x55 = 20.4203522483337
x56 = -29.3215314335047
x57 = 83.7758040957278
x58 = -67.5442420521806
x59 = -98.4365698124802
x60 = 73.8274273593601
x61 = 64.9262481741891
x62 = -10.9955742875643
x63 = -95.8185759344887
x64 = 42.4115008234622
x65 = 95.8185759344887
x66 = 102.101761241668
x67 = 29.845130209103
x68 = -73.8274273593601
x69 = 70.6858347057703
x70 = 83.2522053201295
x71 = -89.5353906273091
x72 = 32.9867228626928
x73 = 90.0589894029074
x74 = -73.3038285837618
x75 = -45.553093477052
x76 = -1.5707963267949
x77 = -86.3937979737193
x78 = 27.2271363311115
x79 = 1.5707963267949
x79 = 1.5707963267949