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sin(2x)+sin(6x)=2cos(2x) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
sin(2*x) + sin(6*x) = 2*cos(2*x)
$$\sin{\left(2 x \right)} + \sin{\left(6 x \right)} = 2 \cos{\left(2 x \right)}$$
Gráfica
Suma y producto de raíces [src]
suma
  3*pi   pi   pi   3*pi
- ---- - -- + -- + ----
   4     4    4     4  
$$\left(\left(- \frac{3 \pi}{4} - \frac{\pi}{4}\right) + \frac{\pi}{4}\right) + \frac{3 \pi}{4}$$
=
0
$$0$$
producto
-3*pi -pi  pi 3*pi
-----*----*--*----
  4    4   4   4  
$$\frac{3 \pi}{4} \frac{\pi}{4} \cdot - \frac{3 \pi}{4} \left(- \frac{\pi}{4}\right)$$
=
    4
9*pi 
-----
 256 
$$\frac{9 \pi^{4}}{256}$$
9*pi^4/256
Respuesta rápida [src]
     -3*pi
x1 = -----
       4  
$$x_{1} = - \frac{3 \pi}{4}$$
     -pi 
x2 = ----
      4  
$$x_{2} = - \frac{\pi}{4}$$
     pi
x3 = --
     4 
$$x_{3} = \frac{\pi}{4}$$
     3*pi
x4 = ----
      4  
$$x_{4} = \frac{3 \pi}{4}$$
x4 = 3*pi/4
Respuesta numérica [src]
x1 = 99.7455667514759
x2 = 50.6581816142042
x3 = -93.8550804799973
x4 = -25.9181393921158
x5 = -35.7356164452618
x6 = -84.037603483527
x7 = -95.4258769753956
x8 = -27.8816347190279
x9 = -55.7632696012188
x10 = 6.67588439275237
x11 = 0.392698983280907
x12 = -20.0276531474781
x13 = 28.6670330605139
x14 = 58.5121630316051
x15 = 72.6493301553909
x16 = 82.4668071567321
x17 = -11.7809724509617
x18 = 60.4756585816035
x19 = 38.484510006475
x20 = 94.6404786968433
x21 = 76.1836218495525
x22 = -10.2101761241668
x23 = -77.7544181763474
x24 = 69.9004365423729
x25 = -80.8960108299372
x26 = 32.2013246992954
x27 = 44.3749961441587
x28 = 11.7809724509617
x29 = 36.5210144564596
x30 = -3.92699081698724
x31 = 74.2201264631339
x32 = -18.0641577581413
x33 = -62.0464549083984
x34 = 66.366144724849
x35 = 14.5298658820215
x36 = 19.2422549276487
x37 = 14.9225651045515
x38 = -13.7444678635645
x39 = 52.228977881506
x40 = -19.6349540849362
x41 = 80.8960108299372
x42 = -29.4524312643322
x43 = -47.9092879672443
x44 = -32.2013246992954
x45 = -90.7134878437654
x46 = -49.4800842940392
x47 = 47.9092879672443
x48 = -58.9048622548086
x49 = 96.2112750446888
x50 = -51.4435798359912
x51 = 23.9546440037767
x52 = -36.9137136796801
x53 = 39.662607278976
x54 = 88.3572933056881
x55 = 77.7544181763474
x56 = 54.1924732744239
x57 = -98.174770424681
x58 = 85.6083998103219
x59 = 55.7632696012188
x60 = 80.5033116073792
x61 = -24.7400419958589
x62 = 8.24668071813848
x63 = -76.1836218495525
x64 = 67.9369411434911
x65 = 84.037603483527
x66 = -68.7223393671189
x67 = 89.9280896986356
x68 = 3.92699081698724
x69 = -65.5807467565488
x70 = -43.5895981768258
x71 = 10.2101761241668
x72 = -7.46128269161422
x73 = 1.96349542914895
x74 = -87.5718953360273
x75 = -69.9004365423729
x76 = -33.7721210260903
x77 = -73.4347284064175
x78 = -54.1924732744239
x79 = -71.863932102205
x80 = 33.7721210260903
x81 = -64.0099503070406
x82 = -21.5984495968768
x83 = -91.8915851175014
x84 = 25.9181393921158
x85 = -79.7179136085933
x86 = 40.0553063332699
x87 = 45.9457925759184
x88 = 91.8915851175014
x89 = -40.0553063332699
x90 = 22.3838475636312
x91 = 98.174770424681
x92 = -57.7267650269417
x93 = 18.0641577581413
x94 = -42.0188017261219
x95 = -14.9225651045515
x96 = -86.0010988907281
x97 = 62.0464549083984
x98 = 30.2378292998339
x99 = -99.7455667514759
x100 = -46.7311907864814
x100 = -46.7311907864814