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(tg(5x)-tg(3x))/(1+tg(5x)tg(3x))=sqrt(3) la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
 tan(5*x) - tan(3*x)      ___
--------------------- = \/ 3 
1 + tan(5*x)*tan(3*x)        
$$\frac{- \tan{\left(3 x \right)} + \tan{\left(5 x \right)}}{\tan{\left(3 x \right)} \tan{\left(5 x \right)} + 1} = \sqrt{3}$$
Gráfica
Suma y producto de raíces [src]
suma
  pi   2*pi
- -- + ----
  3     3  
$$- \frac{\pi}{3} + \frac{2 \pi}{3}$$
=
pi
--
3 
$$\frac{\pi}{3}$$
producto
-pi  2*pi
----*----
 3    3  
$$- \frac{\pi}{3} \frac{2 \pi}{3}$$
=
     2
-2*pi 
------
  9   
$$- \frac{2 \pi^{2}}{9}$$
-2*pi^2/9
Respuesta rápida [src]
     -pi 
x1 = ----
      3  
$$x_{1} = - \frac{\pi}{3}$$
     2*pi
x2 = ----
      3  
$$x_{2} = \frac{2 \pi}{3}$$
x2 = 2*pi/3
Respuesta numérica [src]
x1 = 9.94837673636768
x2 = 57.0722665402146
x3 = -51.3126800086333
x4 = 49.2182849062401
x5 = -90.5825881785057
x6 = 22.5147473507269
x7 = 46.0766922526503
x8 = 88.4881930761125
x9 = 44.5058959258554
x10 = -16.7551608191456
x11 = 19.3731546971371
x12 = 72.7802298081635
x13 = -23.0383461263252
x14 = -35.6047167406843
x15 = -45.0294947014537
x16 = -93.7241808320955
x17 = -73.3038285837618
x18 = 5.23598775598299
x19 = -13.6135681655558
x20 = -27.7507351067098
x21 = 16.2315620435473
x22 = 50.789081233035
x23 = 63.3554518473942
x24 = -85.870199198121
x25 = -37.1755130674792
x26 = 36.6519142918809
x27 = 93.2005820564972
x28 = -95.2949771588904
x29 = 66.497044500984
x30 = 42.9350995990605
x31 = 28.7979326579064
x32 = 96.342174710087
x33 = -8.90117918517108
x34 = -65.4498469497874
x35 = 52.3598775598299
x36 = -74.8746249105567
x37 = -5.75958653158129
x38 = -57.5958653158129
x39 = -82.7286065445312
x40 = -96.8657734856853
x41 = 101.054563690472
x42 = 53.9306738866248
x43 = -89.0117918517108
x44 = 86.9173967493176
x45 = -21.4675497995303
x46 = -100.007366139275
x47 = -56.025068989018
x48 = 71.2094334813686
x49 = -15.1843644923507
x50 = 60.2138591938044
x51 = 82.2050077689329
x52 = 14.6607657167524
x53 = -52.8834763354282
x54 = -87.4409955249159
x55 = 38.2227106186758
x56 = 31.9395253114962
x57 = -78.0162175641465
x58 = 13.0899693899575
x59 = 79.0634151153431
x60 = 20.943951023932
x61 = -34.0339204138894
x62 = 27.2271363311115
x63 = 35.081117965086
x64 = 68.0678408277789
x65 = -30.8923277602996
x66 = 97.9129710368819
x67 = -12.0427718387609
x68 = 74.3510261349584
x69 = 80.634211442138
x70 = 94.7713783832921
x71 = -71.733032256967
x72 = 24.0855436775217
x73 = -41.8879020478639
x74 = 85.3466004225227
x75 = -29.3215314335047
x76 = 30.3687289847013
x77 = -24.60914245312
x78 = 0.523598775598299
x79 = -68.5914396033772
x80 = 8.37758040957278
x81 = -79.5870138909414
x82 = -1.0471975511966
x83 = -43.4586983746588
x84 = -49.7418836818384
x85 = -2.61799387799149
x86 = -81.1578102177363
x87 = -60.7374579694027
x88 = -19.8967534727354
x89 = -38.7463093942741
x90 = 64.9262481741891
x91 = -63.8790506229925
x92 = 2.0943951023932
x93 = -59.1666616426078
x94 = 58.6430628670095
x95 = 90.0589894029074
x96 = 75.9218224617533
x97 = -67.0206432765823
x98 = 41.3643032722656
x99 = -7.33038285837618
x99 = -7.33038285837618