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((3*x^2*cot(x))-(x^3/sin(x)^(2)))=((x^2)*(3*sin(2*x)-2*x)/(2*sin(x)^(2))) la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                  3      2                   
   2             x      x *(3*sin(2*x) - 2*x)
3*x *cot(x) - ------- = ---------------------
                 2                 2         
              sin (x)         2*sin (x)      
$$- \frac{x^{3}}{\sin^{2}{\left(x \right)}} + 3 x^{2} \cot{\left(x \right)} = \frac{x^{2} \left(- 2 x + 3 \sin{\left(2 x \right)}\right)}{2 \sin^{2}{\left(x \right)}}$$
Gráfica
Respuesta rápida [src]
     -3*pi
x1 = -----
       2  
$$x_{1} = - \frac{3 \pi}{2}$$
     -pi 
x2 = ----
      2  
$$x_{2} = - \frac{\pi}{2}$$
     pi
x3 = --
     2 
$$x_{3} = \frac{\pi}{2}$$
     3*pi
x4 = ----
      2  
$$x_{4} = \frac{3 \pi}{2}$$
x4 = 3*pi/2
Suma y producto de raíces [src]
suma
  3*pi   pi   pi   3*pi
- ---- - -- + -- + ----
   2     2    2     2  
$$\left(\left(- \frac{3 \pi}{2} - \frac{\pi}{2}\right) + \frac{\pi}{2}\right) + \frac{3 \pi}{2}$$
=
0
$$0$$
producto
-3*pi -pi  pi 3*pi
-----*----*--*----
  2    2   2   2  
$$\frac{3 \pi}{2} \frac{\pi}{2} \cdot - \frac{3 \pi}{2} \left(- \frac{\pi}{2}\right)$$
=
    4
9*pi 
-----
  16 
$$\frac{9 \pi^{4}}{16}$$
9*pi^4/16
Respuesta numérica [src]
x1 = 48.009593062196
x2 = -26.0
x3 = -60.0045046111821
x4 = 29.5936228899326
x5 = 54.5464024545753
x6 = 82.8342106342491
x7 = -70.7401398316331
x8 = 57.5817086592408
x9 = 26.0
x10 = 23.8522198578906
x11 = 76.2952292064809
x12 = 72.0018927106784
x13 = 56.0827052118761
x14 = -23.8399556348822
x15 = -48.0246385987127
x16 = -19.5833333333333
x17 = -2.0
x18 = -6.98902715002056
x19 = -92.0883192468571
x20 = -83.6281586866413
x21 = -96.1081181102455
x22 = -21.7502316650411
x23 = -87.7450432600703
x24 = 86.0754285595215
x25 = 16.2625406684413
x26 = 98.479012345679
x27 = -57.7496869642518
x28 = -65.517079286467
x29 = 39.9886363636364
x30 = 8.55769230769231
x31 = -7.76445832045655
x32 = 22.2500505735597
x33 = -54.1076970418987
x34 = -79.8173782932099
x35 = 5.99214281367896
x36 = 101.488423798894
x37 = -31.0931711788556
x38 = -43.7538784788869
x39 = 60.273918051834
x40 = -5.625
x41 = 48.2227641418351
x42 = 41.8868163938586
x43 = -23.7010762765226
x44 = -71.6895176373455
x45 = -76.4877192982456
x46 = 67.9690295930102
x47 = -55.9105415860735
x48 = 28.0071120088138
x49 = -93.7610728336562
x50 = 95.8265121973954
x51 = 83.9131944459325
x52 = 58.1688087871478
x53 = -89.7830848559542
x54 = 88.2684299316331
x55 = -77.7507787156012
x56 = 64.2528492134402
x57 = -33.8134328358209
x58 = -14.0092592592593
x59 = 49.9883940974743
x60 = -74.1963226123977
x61 = -45.5758510911427
x62 = 38.3082558680891
x63 = 44.2593406097041
x64 = -64.3971583947135
x65 = 11.9974279835391
x66 = 29.7127836644259
x67 = -99.5341158081144
x68 = -17.8328450864861
x69 = -38.0000240495268
x70 = -85.9891064495496
x71 = 34.1155761024182
x72 = 76.7081218206394
x73 = -81.9703395579907
x74 = -32.691313525098
x75 = 76.741363811336
x76 = 23.6231915934488
x77 = -64.9617907597057
x78 = -49.7557938651299
x79 = 80.1018963309798
x80 = 15.4979454099979
x81 = -11.3904760432775
x82 = 2.0
x83 = 66.332999692031
x84 = -51.689015573584
x85 = -9.79673913043478
x86 = 70.2399267399267
x87 = 57.4194532865197
x88 = -3.75
x89 = -28.0174116659548
x90 = 4.23333333333333
x91 = 18.0605147426287
x92 = -41.8238738478208
x93 = 92.3669280697192
x94 = -91.9433107636577
x95 = 10.2667824074074
x96 = 90.1500960283763
x97 = -39.7090909090909
x98 = 94.0011303366035
x98 = 94.0011303366035