ctg2x/3=0 (уравнение)

Найду корень уравнения: ctg2x/3=0

Вы ввели

cot(2*x)    
-------- = 0
   3        

$$\frac{\cot{\left(2 x \right)}}{3} = 0$$

Подробное решение

Дано уравнение
$$\frac{\cot{\left(2 x \right)}}{3} = 0$$
преобразуем
$$\frac{\cot{\left(2 x \right)}}{3} - 1 = 0$$
$$\frac{\cot{\left(2 x \right)}}{3} - 1 = 0$$
Сделаем замену
$$w = \cot{\left(2 x \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$\frac{w}{3} = 1$$
Разделим обе части ур-ния на 1/3

w = 1 / (1/3)

Получим ответ: w = 3
делаем обратную замену
$$\cot{\left(2 x \right)} = w$$
подставляем w:

Быстрый ответ

     pi
x1 = --
     4 

$$x_{1} = \frac{\pi}{4}$$

Сумма и произведение корней

сумма

    pi
0 + --
    4 

$$0 + \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

произведение

  pi
1*--
  4 

$$1 \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

Численный ответ

x1 = -65.1880475619882

x2 = 68.329640215578

x3 = -41.6261026600648

x4 = 3.92699081698724

x5 = 16.4933614313464

x6 = 30.6305283725005

x7 = 11.7809724509617

x8 = -40.0553063332699

x9 = 8.63937979737193

x10 = 88.7499924639117

x11 = -35.3429173528852

x12 = 10.2101761241668

x13 = 27.4889357189107

x14 = -5.49778714378214

x15 = 32.2013246992954

x16 = -27.4889357189107

x17 = 24.3473430653209

x18 = 44.7676953136546

x19 = -38.484510006475

x20 = -62.0464549083984

x21 = -68.329640215578

x22 = 46.3384916404494

x23 = 66.7588438887831

x24 = -43.1968989868597

x25 = 19.6349540849362

x26 = -69.9004365423729

x27 = -55.7632696012188

x28 = 84.037603483527

x29 = 54.1924732744239

x30 = 90.3207887907066

x31 = -79.3252145031423

x32 = 22.776546738526

x33 = 60.4756585816035

x34 = -24.3473430653209

x35 = 5.49778714378214

x36 = -7.06858347057703

x37 = -63.6172512351933

x38 = 47.9092879672443

x39 = 52.621676947629

x40 = 98.174770424681

x41 = -90.3207887907066

x42 = 36.9137136796801

x43 = -47.9092879672443

x44 = 49.4800842940392

x45 = -91.8915851175014

x46 = -10.2101761241668

x47 = -54.1924732744239

x48 = 2.35619449019234

x49 = 80.8960108299372

x50 = -33.7721210260903

x51 = -18.0641577581413

x52 = -60.4756585816035

x53 = 76.1836218495525

x54 = 77.7544181763474

x55 = -99.7455667514759

x56 = -30.6305283725005

x57 = -77.7544181763474

x58 = 71.4712328691678

x59 = 14.9225651045515

x60 = -93.4623814442964

x61 = -57.3340659280137

x62 = -85.6083998103219

x63 = -3.92699081698724

x64 = -19.6349540849362

x65 = -16.4933614313464

x66 = -32.2013246992954

x67 = 91.8915851175014

x68 = 69.9004365423729

x69 = 58.9048622548086

x70 = 38.484510006475

x71 = -82.4668071567321

x72 = -98.174770424681

x73 = -21.2057504117311

x74 = 41.6261026600648

x75 = 55.7632696012188

x76 = -52.621676947629

x77 = -11.7809724509617

x78 = 62.0464549083984

x79 = 82.4668071567321

x80 = -25.9181393921158

x81 = -71.4712328691678

x82 = 18.0641577581413

x83 = 93.4623814442964

x84 = -96.6039740978861

x85 = -74.6128255227576

x86 = 99.7455667514759

x87 = -2.35619449019234

x88 = 63.6172512351933

x89 = -76.1836218495525

x90 = -46.3384916404494

x91 = 85.6083998103219

x92 = 25.9181393921158

x93 = -84.037603483527

x94 = 33.7721210260903

x95 = -49.4800842940392

x96 = 40.0553063332699

x97 = 96.6039740978861

x98 = -13.3517687777566

x99 = 74.6128255227576

x100 = -87.1791961371168

График