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(tan(x)+tan(2*x))/(1-tan(x)*tan(2*x))=1 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
 tan(x) + tan(2*x)     
------------------- = 1
1 - tan(x)*tan(2*x)    
tan(x)+tan(2x)tan(x)tan(2x)+1=1\frac{\tan{\left(x \right)} + \tan{\left(2 x \right)}}{- \tan{\left(x \right)} \tan{\left(2 x \right)} + 1} = 1
Gráfica
0-80-60-40-2020406080-100100-50005000
Suma y producto de raíces [src]
suma
  11*pi   7*pi   pi   5*pi
- ----- - ---- + -- + ----
    12     12    12    12 
((11π127π12)+π12)+5π12\left(\left(- \frac{11 \pi}{12} - \frac{7 \pi}{12}\right) + \frac{\pi}{12}\right) + \frac{5 \pi}{12}
=
-pi
π- \pi
producto
-11*pi -7*pi pi 5*pi
------*-----*--*----
  12     12  12  12 
5π12π1211π12(7π12)\frac{5 \pi}{12} \frac{\pi}{12} \cdot - \frac{11 \pi}{12} \left(- \frac{7 \pi}{12}\right)
=
      4
385*pi 
-------
 20736 
385π420736\frac{385 \pi^{4}}{20736}
385*pi^4/20736
Respuesta rápida [src]
     -11*pi
x1 = ------
       12  
x1=11π12x_{1} = - \frac{11 \pi}{12}
     -7*pi
x2 = -----
       12 
x2=7π12x_{2} = - \frac{7 \pi}{12}
     pi
x3 = --
     12
x3=π12x_{3} = \frac{\pi}{12}
     5*pi
x4 = ----
      12 
x4=5π12x_{4} = \frac{5 \pi}{12}
x4 = 5*pi/12
Respuesta numérica [src]
x1 = 18.0641577581413
x2 = 52.621676947629
x3 = -93.9859802198946
x4 = -15.4461638801498
x5 = 28.5361332701073
x6 = 6.54498469497874
x7 = -33.248522250492
x8 = -69.9004365423729
x9 = 26.4417381677141
x10 = 46.3384916404494
x11 = 34.8193185772869
x12 = 56.8104671524154
x13 = -53.1452757232273
x14 = 48.4328867428426
x15 = 36.9137136796801
x16 = -74.0892267471593
x17 = -37.4373124552784
x18 = 30.6305283725005
x19 = -91.8915851175014
x20 = -30.1069295969022
x21 = -39.5317075576716
x22 = -50.0036830696375
x23 = -65.7116463375865
x24 = 86.1319985859202
x25 = -75.1364242983559
x26 = -71.9948316447661
x27 = 81.9432083811338
x28 = 10.7337748997651
x29 = -83.5140047079287
x30 = 76.7072206251508
x31 = -52.0980781720307
x32 = -89.7971900151083
x33 = 4.45058959258554
x34 = -96.0803753222878
x35 = 54.7160720500222
x36 = -19.6349540849362
x37 = 68.329640215578
x38 = 78.801615727544
x39 = -57.3340659280137
x40 = 94.5095789954929
x41 = -85.6083998103219
x42 = -47.9092879672443
x43 = 37.9609112308767
x44 = -59.4284610304069
x45 = 50.5272818452358
x46 = 40.0553063332699
x47 = 0.261799387799149
x48 = -31.1541271480988
x49 = 88.2263936883134
x50 = -67.8060414399797
x51 = 8.63937979737193
x52 = 15.9697626557481
x53 = -79.3252145031423
x54 = 44.2440965380563
x55 = -17.540558982543
x56 = 24.3473430653209
x57 = -25.9181393921158
x58 = -21.7293491873294
x59 = -55.2396708256205
x60 = 66.2352451131848
x61 = -13.3517687777566
x62 = -97.1275728734844
x63 = -77.2308194007491
x64 = -99.2219679758776
x65 = 90.3207887907066
x66 = -45.8148928648512
x67 = 13.8753675533549
x68 = -35.3429173528852
x69 = -3.92699081698724
x70 = 32.7249234748937
x71 = -87.7027949127151
x72 = -28.012534494509
x73 = -1.83259571459405
x74 = 92.4151838930998
x75 = -41.6261026600648
x76 = 2.35619449019234
x77 = -8.11578102177363
x78 = 12.8281700021583
x79 = -81.4196096055355
x80 = 58.9048622548086
x81 = 72.5184304203644
x82 = 59.9520598060052
x83 = 100.792764302673
x84 = 80.8960108299372
x85 = 70.4240353179712
x86 = 22.2529479629277
x87 = 42.1497014356631
x88 = -6.02138591938044
x89 = 74.6128255227576
x90 = -23.8237442897226
x91 = -43.720497762458
x92 = 64.1408500107916
x93 = 62.0464549083984
x94 = 98.6983692002793
x95 = 20.1585528605345
x96 = 96.6039740978861
x97 = -63.6172512351933
x98 = -11.2573736753634
x99 = 84.037603483527
x100 = -9.16297857297023
x101 = -61.5228561328001
x101 = -61.5228561328001