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4*cos(2*x)*cos(3*x)+3=6*sin(2*x+3*pi/2)+2*(-cos(3*x)) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                               /      3*pi\                
4*cos(2*x)*cos(3*x) + 3 = 6*sin|2*x + ----| + 2*(-cos(3*x))
                               \       2  /
$$4 \cos{\left(2 x \right)} \cos{\left(3 x \right)} + 3 = 6 \sin{\left(2 x + \frac{3 \pi}{2} \right)} + 2 \left(- \cos{\left(3 x \right)}\right)$$
Simplificar
Gráfica
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                /     /  ___\\         /     /  ___\\         /     /  ___\\         /     /  ___\\
  pi   pi   2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //     2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //
- -- + -- + ------------------ - -------------------- + - ------------------ + --------------------
  3    3            3                     3                       3                     3
$$\left(\left(- \frac{\pi}{3} + \frac{\pi}{3}\right) + \left(\frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} - \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}\right)\right) + \left(- \frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} + \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}\right)$$ 
=
0
$$0$$ 
producto
        /    /     /  ___\\         /     /  ___\\\ /      /     /  ___\\         /     /  ___\\\
-pi  pi |2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //| |  2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //|
----*--*|------------------ - --------------------|*|- ------------------ + --------------------|
 3   3  \        3                     3          / \          3                     3          /
$$- \frac{\pi}{3} \frac{\pi}{3} \left(\frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} - \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}\right) \left(- \frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} + \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}\right)$$ 
=
                                               2
    2 /      /     /  ___\\     /     /  ___\\\ 
4*pi *\- I*re\atanh\\/ 5 // + im\atanh\\/ 5 /// 
------------------------------------------------
                       81
$$\frac{4 \pi^{2} \left(\operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)} - i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}\right)^{2}}{81}$$ 
4*pi^2*(-i*re(atanh(sqrt(5))) + im(atanh(sqrt(5))))^2/81
Respuesta rápida [src] 
     -pi 
x1 = ----
      3
$$x_{1} = - \frac{\pi}{3}$$ 
     pi
x2 = --
     3
$$x_{2} = \frac{\pi}{3}$$ 
         /     /  ___\\         /     /  ___\\
     2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //
x3 = ------------------ - --------------------
             3                     3
$$x_{3} = \frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} - \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}$$ 
           /     /  ___\\         /     /  ___\\
       2*im\atanh\\/ 5 //   2*I*re\atanh\\/ 5 //
x4 = - ------------------ + --------------------
               3                     3
$$x_{4} = - \frac{2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3} + \frac{2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{5} \right)}\right)}}{3}$$ 
x4 = -2*im(atanh(sqrt(5)))/3 + 2*i*re(atanh(sqrt(5)))/3
Respuesta numérica [src] 
x1 = 30.3687289847013
x2 = 89.0117918517108
x3 = -83.7758040957278
x4 = 36.6519142918809
x5 = 10985.1023120523
x6 = 76.4454212373516
x7 = 32.4631240870945
x8 = 74.3510261349584
x9 = 105.766952670856
x10 = -5.23598775598299
x11 = 4.18879020478639
x12 = 80.634211442138
x13 = -96.342174710087
x14 = -76.4454212373516
x15 = 24.0855436775217
x16 = -55.5014702134197
x17 = -39.7935069454707
x18 = 2.0943951023932
x19 = -7.33038285837618
x20 = 112.050137978036
x21 = 83.7758040957278
x22 = -61.7846555205993
x23 = 68.0678408277789
x24 = -35.6047167406843
x25 = -41.8879020478639
x26 = -82.7286065445312
x27 = -85.870199198121
x28 = -79.5870138909414
x29 = -893.259511170698
x30 = -51.3126800086333
x31 = -45.0294947014537
x32 = 52.3598775598299
x33 = -42.9350995990605
x34 = 23.0383461263252
x35 = 11.5191730631626
x36 = -30.3687289847013
x37 = 93.2005820564972
x38 = 54.4542726622231
x39 = 85.870199198121
x40 = 13365.3823459222
x41 = -32.4631240870945
x42 = -49.2182849062401
x43 = -24.0855436775217
x44 = -48.1710873550435
x45 = -68.0678408277789
x46 = 1.0471975511966
x47 = 96.342174710087
x48 = -36.6519142918809
x49 = -11.5191730631626
x50 = 39.7935069454707
x51 = -52.3598775598299
x52 = -17.8023583703422
x53 = 82.7286065445312
x54 = 55.5014702134197
x55 = 38.7463093942741
x56 = 99.4837673636768
x57 = 92.1533845053006
x58 = -19.8967534727354
x59 = 61.7846555205993
x60 = 13.6135681655558
x61 = -57.5958653158129
x62 = -2.0943951023932
x63 = -26.1799387799149
x64 = -70.162235930172
x65 = 46.0766922526503
x66 = 17.8023583703422
x67 = 49.2182849062401
x68 = -90.0589894029074
x69 = 48.1710873550435
x70 = 41.8879020478639
x71 = 10.471975511966
x72 = -2040.98802728217
x73 = 70.162235930172
x74 = -92.1533845053006
x75 = -13.6135681655558
x76 = -225.147473507269
x77 = -38.7463093942741
x78 = 98.4365698124802
x79 = 57.5958653158129
x80 = -95.2949771588904
x81 = 90.0589894029074
x82 = -99.4837673636768
x83 = 5.23598775598299
x84 = -63.8790506229925
x85 = 19.8967534727354
x86 = -93.2005820564972
x87 = -33.5103216382911
x88 = -4.18879020478639
x89 = -117.286125734019
x90 = 63.8790506229925
x91 = -74.3510261349584
x92 = -46.0766922526503
x93 = 8.37758040957278
x94 = 45.0294947014537
x95 = 26.1799387799149
x96 = -77.4926187885482
x96 = -77.4926187885482
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