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tgx+tg4x=tg2x+tg3x la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
tan(x) + tan(4*x) = tan(2*x) + tan(3*x)
$$\tan{\left(x \right)} + \tan{\left(4 x \right)} = \tan{\left(2 x \right)} + \tan{\left(3 x \right)}$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
  4*pi   3*pi   2*pi   pi   pi   2*pi   3*pi   4*pi     
- ---- - ---- - ---- - -- + -- + ---- + ---- + ---- + pi
   5      5      5     5    5     5      5      5
$$\left(\left(\left(\left(\left(\left(\left(- \frac{4 \pi}{5} - \frac{3 \pi}{5}\right) - \frac{2 \pi}{5}\right) - \frac{\pi}{5}\right) + \frac{\pi}{5}\right) + \frac{2 \pi}{5}\right) + \frac{3 \pi}{5}\right) + \frac{4 \pi}{5}\right) + \pi$$ 
=
pi
$$\pi$$ 
producto
  -4*pi -3*pi -2*pi -pi  pi 2*pi 3*pi 4*pi   
0*-----*-----*-----*----*--*----*----*----*pi
    5     5     5    5   5   5    5    5
$$\pi \frac{4 \pi}{5} \frac{3 \pi}{5} \frac{2 \pi}{5} \frac{\pi}{5} \cdot - \frac{\pi}{5} \cdot - \frac{2 \pi}{5} \cdot - \frac{3 \pi}{5} \cdot 0 \left(- \frac{4 \pi}{5}\right)$$ 
=
0
$$0$$ 
0
Respuesta rápida [src] 
x1 = 0
$$x_{1} = 0$$ 
     -4*pi
x2 = -----
       5
$$x_{2} = - \frac{4 \pi}{5}$$ 
     -3*pi
x3 = -----
       5
$$x_{3} = - \frac{3 \pi}{5}$$ 
     -2*pi
x4 = -----
       5
$$x_{4} = - \frac{2 \pi}{5}$$ 
     -pi 
x5 = ----
      5
$$x_{5} = - \frac{\pi}{5}$$ 
     pi
x6 = --
     5
$$x_{6} = \frac{\pi}{5}$$ 
     2*pi
x7 = ----
      5
$$x_{7} = \frac{2 \pi}{5}$$ 
     3*pi
x8 = ----
      5
$$x_{8} = \frac{3 \pi}{5}$$ 
     4*pi
x9 = ----
      5
$$x_{9} = \frac{4 \pi}{5}$$ 
x10 = pi
$$x_{10} = \pi$$ 
x10 = pi
Respuesta numérica [src] 
x1 = 84.1946831162065
x2 = 98.0176907920015
x3 = -42.0973415581032
x4 = 18.2212373908208
x5 = -98.0176907920015
x6 = -65.9734548486986
x7 = 21.9911516466404
x8 = 20.1061929829747
x9 = 86.0796387083603
x10 = -57.8053048260522
x11 = -15.707974359936
x12 = 94.2477801895162
x13 = -83.5663645854885
x14 = -37.6991253259725
x15 = 8.16814089933346
x16 = 62.2035345410779
x17 = 40.2123859659494
x18 = -96.1327351998477
x19 = -59.6902763293664
x20 = 0.0
x21 = 89.2212313619501
x22 = 58.4336233567702
x23 = 36.4424747816416
x24 = -91.734505484822
x25 = -64.0884901332318
x26 = 54.6637121724624
x27 = 28.2743274943129
x28 = -81.6814273793448
x29 = 87.9646065891021
x30 = 25.132766994109
x31 = 5.02654824574367
x32 = -45.867252742411
x33 = 30.159289474462
x34 = -69.7433569096934
x35 = 72.2566292948604
x36 = 65.973454934889
x37 = -13.8230076757951
x38 = -9.42481832724324
x39 = -43.9823032737618
x40 = -1.88495559215388
x41 = -35.8141562509236
x42 = -47.7522083345649
x43 = 10.0530964914873
x44 = -87.9646063065009
x45 = -25.7610597594363
x46 = -30.159289474462
x47 = 42.0973415581032
x48 = -3.76991118430775
x49 = 50.2654783980164
x50 = -18.2212373908208
x51 = 40.8407145452695
x52 = -19.4778744522567
x53 = -33.9292006587698
x54 = -38.9557489045134
x55 = -74.1415866247191
x56 = 6.28317657745173
x57 = -99.9026463841554
x58 = -79.7964534011807
x59 = -61.5752160103599
x60 = 14.451326206513
x61 = -7.5398223686155
x62 = -52.1504380495906
x63 = 64.0884901332318
x64 = 64.7168086639497
x65 = -23.8761041672824
x66 = 32.6725635973338
x67 = -89.8495498926681
x68 = -21.9911516456241
x69 = -11.9380520836412
x70 = 80.4247719318987
x71 = 91.734505484822
x72 = -67.8584013175395
x73 = 51.5221195188726
x74 = 43.9823032903129
x75 = 75.3982079073418
x75 = 75.3982079073418
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