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ctg(x)=(3^1/3)/3 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
         3 ___
         \/ 3 
cot(x) = -----
           3  
$$\cot{\left(x \right)} = \frac{\sqrt[3]{3}}{3}$$
Solución detallada
Tenemos la ecuación
$$\cot{\left(x \right)} = \frac{\sqrt[3]{3}}{3}$$
cambiamos
$$\cot{\left(x \right)} - 1 - \frac{\sqrt[3]{3}}{3} = 0$$
$$\cot{\left(x \right)} - 1 - \frac{\sqrt[3]{3}}{3} = 0$$
Sustituimos
$$w = \cot{\left(x \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 + w - 3^1/3/3 = 0

Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w - \frac{\sqrt[3]{3}}{3} = 1$$
Dividamos ambos miembros de la ecuación en (w - 3^(1/3)/3)/w
w = 1 / ((w - 3^(1/3)/3)/w)

Obtenemos la respuesta: w = 1 + 3^(1/3)/3
hacemos cambio inverso
$$\cot{\left(x \right)} = w$$
sustituimos w:
Gráfica
Respuesta rápida [src]
         /3 ___\
         |\/ 3 |
x1 = acot|-----|
         \  3  /
$$x_{1} = \operatorname{acot}{\left(\frac{\sqrt[3]{3}}{3} \right)}$$
x1 = acot(3^(1/3)/3)
Suma y producto de raíces [src]
suma
    /3 ___\
    |\/ 3 |
acot|-----|
    \  3  /
$$\operatorname{acot}{\left(\frac{\sqrt[3]{3}}{3} \right)}$$
=
    /3 ___\
    |\/ 3 |
acot|-----|
    \  3  /
$$\operatorname{acot}{\left(\frac{\sqrt[3]{3}}{3} \right)}$$
producto
    /3 ___\
    |\/ 3 |
acot|-----|
    \  3  /
$$\operatorname{acot}{\left(\frac{\sqrt[3]{3}}{3} \right)}$$
=
    /3 ___\
    |\/ 3 |
acot|-----|
    \  3  /
$$\operatorname{acot}{\left(\frac{\sqrt[3]{3}}{3} \right)}$$
acot(3^(1/3)/3)
Respuesta numérica [src]
x1 = 16.8306303564336
x2 = -11.4437035258745
x3 = -96.2667051727989
x4 = -17.7268888330541
x5 = -49.142815368952
x6 = 26.255408317203
x7 = -55.4260006761316
x8 = 1.12266708848468
x9 = -71.1339639440806
x10 = 54.5297421995112
x11 = -86.8419272120295
x12 = 70.2377054674601
x13 = 98.5120393497683
x14 = 19.9722230100234
x15 = 63.9545201602805
x16 = 57.671334853101
x17 = -39.7180374081826
x18 = 67.0961128138703
x19 = 82.8040760818193
x20 = -27.1516667938235
x21 = 48.2465568923316
x22 = -61.7091859833112
x23 = -8.3021108722847
x24 = -20.8684814866439
x25 = 76.5208907746397
x26 = 95.3704466961785
x27 = 41.963371585152
x28 = -67.9923712904908
x29 = -36.5764447545928
x30 = 29.3970009707928
x31 = -33.434852101003
x32 = 79.6624834282295
x33 = 45.1049642387418
x34 = -14.5852961794643
x35 = -42.8596300617724
x36 = -93.1251125192091
x37 = -58.5675933297214
x38 = -52.2844080225418
x39 = -99.4082978263887
x40 = 4.26425974207448
x41 = 10.5474450492541
x42 = -30.2932594474132
x43 = 35.6801862779724
x44 = -2.01892556510511
x45 = -89.9835198656193
x46 = 89.0872613889989
x47 = 92.2288540425887
x48 = 51.3881495459214
x49 = 85.9456687354091
x50 = -24.0100741402337
x51 = 60.8129275066908
x52 = -77.4171492512601
x53 = -83.7003345584397
x54 = -64.850778636901
x55 = 73.3792981210499
x56 = -46.0012227153622
x57 = 13.6890377028439
x58 = 32.5385936243826
x59 = 7.40585239566427
x60 = 23.1138156636132
x61 = -74.2755565976704
x62 = -80.5587419048499
x63 = -5.1605182186949
x64 = 38.8217789315622
x64 = 38.8217789315622