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sin(3x)+sin(4x)+sin(5x)=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
sin(3*x) + sin(4*x) + sin(5*x) = 0
$$\left(\sin{\left(3 x \right)} + \sin{\left(4 x \right)}\right) + \sin{\left(5 x \right)} = 0$$
Gráfica
Respuesta rápida [src]
x1 = 0
$$x_{1} = 0$$
     -3*pi
x2 = -----
       4  
$$x_{2} = - \frac{3 \pi}{4}$$
     -2*pi
x3 = -----
       3  
$$x_{3} = - \frac{2 \pi}{3}$$
     -pi 
x4 = ----
      2  
$$x_{4} = - \frac{\pi}{2}$$
     -pi 
x5 = ----
      4  
$$x_{5} = - \frac{\pi}{4}$$
     pi
x6 = --
     4 
$$x_{6} = \frac{\pi}{4}$$
     pi
x7 = --
     2 
$$x_{7} = \frac{\pi}{2}$$
     2*pi
x8 = ----
      3  
$$x_{8} = \frac{2 \pi}{3}$$
     3*pi
x9 = ----
      4  
$$x_{9} = \frac{3 \pi}{4}$$
x10 = pi
$$x_{10} = \pi$$
x10 = pi
Suma y producto de raíces [src]
suma
  3*pi   2*pi   pi   pi   pi   pi   2*pi   3*pi     
- ---- - ---- - -- - -- + -- + -- + ---- + ---- + pi
   4      3     2    4    4    2     3      4       
$$\left(\left(\left(\left(\left(\left(\left(- \frac{3 \pi}{4} - \frac{2 \pi}{3}\right) - \frac{\pi}{2}\right) - \frac{\pi}{4}\right) + \frac{\pi}{4}\right) + \frac{\pi}{2}\right) + \frac{2 \pi}{3}\right) + \frac{3 \pi}{4}\right) + \pi$$
=
pi
$$\pi$$
producto
  -3*pi -2*pi -pi  -pi  pi pi 2*pi 3*pi   
0*-----*-----*----*----*--*--*----*----*pi
    4     3    2    4   4  2   3    4     
$$\pi \frac{3 \pi}{4} \frac{2 \pi}{3} \frac{\pi}{2} \frac{\pi}{4} \cdot - \frac{\pi}{4} \cdot - \frac{\pi}{2} \cdot - \frac{2 \pi}{3} \cdot 0 \left(- \frac{3 \pi}{4}\right)$$
=
0
$$0$$
0
Respuesta numérica [src]
x1 = 65.9734457253857
x2 = -23.5619449019235
x3 = -79.5870138909414
x4 = -29.845130209103
x5 = -21.9911485751286
x6 = -11.7809724509617
x7 = 21.9911485751286
x8 = -85.870199198121
x9 = -15.707963267949
x10 = -4.18879020478639
x11 = 40.0553063332699
x12 = -32.2013246992954
x13 = -25.9181393921158
x14 = 36.1283155162826
x15 = 6.28318530717959
x16 = 2.0943951023932
x17 = 33.5103216382911
x18 = 54.9778714378214
x19 = -18.0641577581413
x20 = 39.2699081698724
x21 = 64.4026493985908
x22 = -69.9004365423729
x23 = -39.7935069454707
x24 = -95.8185759344887
x25 = 28.2743338823081
x26 = 18.0641577581413
x27 = 76.1836218495525
x28 = -62.0464549083984
x29 = 73.8274273593601
x30 = 32.2013246992954
x31 = 62.0464549083984
x32 = -33.7721210260903
x33 = -63.6172512351933
x34 = -10.2101761241668
x35 = -90.0589894029074
x36 = -47.9092879672443
x37 = -41.8879020478639
x38 = 85.6083998103219
x39 = 10.2101761241668
x40 = 60.7374579694027
x41 = -2.0943951023932
x42 = 41.8879020478639
x43 = 72.2566310325652
x44 = 24.3473430653209
x45 = -51.8362787842316
x46 = 58.1194640914112
x47 = -76.1836218495525
x48 = -73.8274273593601
x49 = -87.9645943005142
x50 = -37.6991118430775
x51 = -43.9822971502571
x52 = 29.845130209103
x53 = -45.553093477052
x54 = 98.174770424681
x55 = 8.63937979737193
x56 = -54.1924732744239
x57 = -35.3429173528852
x58 = 80.1106126665397
x59 = -58.1194640914112
x60 = -98.174770424681
x61 = 77.4926187885482
x62 = 8.37758040957278
x63 = 52.3598775598299
x64 = -81.6814089933346
x65 = -46.0766922526503
x66 = 16.7551608191456
x67 = -65.9734457253857
x68 = 0.0
x69 = -67.5442420521806
x70 = -91.8915851175014
x71 = 96.342174710087
x72 = 77.7544181763474
x73 = 43.9822971502571
x74 = -83.7758040957278
x75 = 25.9181393921158
x76 = -7.85398163397448
x77 = -55.7632696012188
x78 = -19.6349540849362
x79 = -14.1371669411541
x80 = 50.2654824574367
x81 = 94.2477796076938
x82 = -3.92699081698724
x83 = 48.1710873550435
x84 = -77.7544181763474
x85 = 4.18879020478639
x86 = -59.6902604182061
x87 = -104.457955731861
x88 = 109.955742875643
x89 = 14.1371669411541
x90 = 69.9004365423729
x91 = 20.4203522483337
x92 = 54.1924732744239
x93 = 92.1533845053006
x94 = 46.0766922526503
x95 = 87.9645943005142
x96 = 84.037603483527
x97 = 68.329640215578
x98 = -71.4712328691678
x99 = -99.7455667514759
x99 = -99.7455667514759