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tg(2x−4)6=3√3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                     ___
tan(2*x - 4)*6 = 3*\/ 3
6tan⁡(2x−4)=336 \tan{\left(2 x - 4 \right)} = 3 \sqrt{3}
Simplificar
Solución detallada
Tenemos la ecuación
6tan⁡(2x−4)=336 \tan{\left(2 x - 4 \right)} = 3 \sqrt{3}
es la ecuación trigonométrica más simple
Dividamos ambos miembros de la ecuación en 6

La ecuación se convierte en
tan⁡(2x−4)=32\tan{\left(2 x - 4 \right)} = \frac{\sqrt{3}}{2}
Esta ecuación se reorganiza en
2x−4=πn+atan⁡(32)2 x - 4 = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}
O
2x−4=πn+atan⁡(32)2 x - 4 = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}
, donde n es cualquier número entero
Transportemos
−4-4
al miembro derecho de la ecuación
con el signo opuesto, en total:
2x=πn+atan⁡(32)+42 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)} + 4
Dividamos ambos miembros de la ecuación obtenida en
22
obtenemos la respuesta:
x1=πn2+atan⁡(32)2+2x_{1} = \frac{\pi n}{2} + \frac{\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}}{2} + 2
Gráfica
0-80-60-40-2020406080-100100-50000005000000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
             /  ___\
             |\/ 3 |
         atan|-----|
             \  2  /
x1 = 2 + -----------
              2
x1=atan⁡(32)2+2x_{1} = \frac{\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}}{2} + 2 
x1 = atan(sqrt(3)/2)/2 + 2
Suma y producto de raíces [src] 
suma
        /  ___\
        |\/ 3 |
    atan|-----|
        \  2  /
2 + -----------
         2
atan⁡(32)2+2\frac{\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}}{2} + 2 
=
        /  ___\
        |\/ 3 |
    atan|-----|
        \  2  /
2 + -----------
         2
atan⁡(32)2+2\frac{\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}}{2} + 2 
producto
        /  ___\
        |\/ 3 |
    atan|-----|
        \  2  /
2 + -----------
         2
atan⁡(32)2+2\frac{\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}}{2} + 2 
=
        /  ___\
        |\/ 3 |
    atan|-----|
        \  2  /
2 + -----------
         2
atan⁡(32)2+2\frac{\operatorname{atan}{\left(\frac{\sqrt{3}}{2} \right)}}{2} + 2 
2 + atan(sqrt(3)/2)/2
Respuesta numérica [src] 
x1 = -25.9174716928358
x2 = -32.2006570000153
x3 = -33.7714533268102
x4 = -7.067915771297
x5 = 96.6046417971662
x6 = 46.3391593397295
x7 = -54.1918055751439
x8 = -87.1785284378367
x9 = 90.3214564899866
x10 = -44.7670276143745
x11 = 38.485177705755
x12 = 54.193140973704
x13 = 76.1842895488325
x14 = 24.3480107646009
x15 = -88.7493247646316
x16 = -57.3333982287337
x17 = -40.0546386339898
x18 = -51.0502129215541
x19 = 33.7727887253703
x20 = 66.7595115880631
x21 = 77.7550858756274
x22 = -58.9041945555286
x23 = -71.4705651698878
x24 = -65.1873798627082
x25 = 21.2064181110111
x26 = -63.6165835359133
x27 = 30.6311960717805
x28 = -62.0457872091184
x29 = -47.9086202679643
x30 = -69.8997688430929
x31 = 95.0338454703713
x32 = 36.9143813789601
x33 = 18.0648254574213
x34 = -5.4971194445021
x35 = -84.0369357842469
x36 = 22.777214437806
x37 = -11.7803047516817
x38 = -22.775879039246
x39 = 98.1754381239611
x40 = 8.64004749665197
x41 = -95.0325100718112
x42 = -76.1829541502725
x43 = 60.4763262808836
x44 = 91.8922528167815
x45 = -49.4794165947592
x46 = -79.3245468038622
x47 = -66.7581761895031
x48 = 69.9011042416529
x49 = 29.0603997449856
x50 = -77.7537504770673
x51 = 68.330307914858
x52 = 11.7816401502418
x53 = -43.1962312875796
x54 = 0.786065862677486
x55 = -93.4617137450163
x56 = -99.7448990521959
x57 = 3.92765851626728
x58 = 80.8966785292172
x59 = 7.06925116985707
x60 = -91.8909174182214
x61 = -55.7626019019388
x62 = 58.9055299540887
x63 = -13.3511010784766
x64 = 32.2019923985754
x65 = -73.0413614966827
x66 = -10.2095084248868
x67 = 47.9099556665244
x68 = -21.2050827124511
x69 = 52.6223446469091
x70 = -19.6342863856562
x71 = -85.6077321110418
x72 = 55.7639373004989
x73 = 74.6134932220376
x74 = 40.0559740325499
x75 = -0.78473046411741
x76 = -98.174102725401
x77 = 14.9232328038316
x78 = 65.1887152612682
x79 = 99.746234450756
x80 = 88.7506601631917
x81 = -36.9130459804
x82 = -41.6254349607847
x83 = 25.9188070913958
x84 = 44.7683630129346
x85 = -80.8953431306571
x86 = -35.3422496536051
x87 = 43.1975666861397
x88 = 2.35686218947238
x89 = -3.9263231177072
x90 = 62.0471226076785
x91 = -14.9218974052715
x92 = 51.0515483201142
x93 = 87.1798638363968
x94 = 16.4940291306265
x95 = -27.4882680196307
x96 = 84.038271182807
x97 = 73.0426968952427
x98 = 10.2108438234469
x99 = -29.0590643464256
x100 = 82.4674748560121
x101 = -18.0634900588613
x101 = -18.0634900588613
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