ctg(4-3x)=2 (уравнение)

Найду корень уравнения: ctg(4-3x)=2

Вы ввели

cot(4 - 3*x) = 2

$$\cot{\left(4 - 3 x \right)} = 2$$

Подробное решение

Дано уравнение
$$\cot{\left(4 - 3 x \right)} = 2$$
преобразуем
$$- \cot{\left(3 x - 4 \right)} - 2 = 0$$
$$- \cot{\left(3 x - 4 \right)} - 2 = 0$$
Сделаем замену
$$w = \cot{\left(3 x - 4 \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$- w = 2$$
Разделим обе части ур-ния на -1

w = 2 / (-1)

Получим ответ: w = -2
делаем обратную замену
$$\cot{\left(3 x - 4 \right)} = w$$
подставляем w:

Быстрый ответ

     4   acot(2)
x1 = - - -------
     3      3   

$$x_{1} = \frac{4}{3} - \frac{\operatorname{acot}{\left(2 \right)}}{3}$$

Сумма и произведение корней

сумма

    4   acot(2)
0 + - - -------
    3      3   

$$0 + \left(\frac{4}{3} - \frac{\operatorname{acot}{\left(2 \right)}}{3}\right)$$

=

4   acot(2)
- - -------
3      3   

$$\frac{4}{3} - \frac{\operatorname{acot}{\left(2 \right)}}{3}$$

произведение

  /4   acot(2)\
1*|- - -------|
  \3      3   /

$$1 \cdot \left(\frac{4}{3} - \frac{\operatorname{acot}{\left(2 \right)}}{3}\right)$$

=

4   acot(2)
- - -------
3      3   

$$\frac{4}{3} - \frac{\operatorname{acot}{\left(2 \right)}}{3}$$

Численный ответ

x1 = 15.8395498470854

x2 = 66.1050323045221

x3 = -73.1722420046254

x4 = -7.19879627923972

x5 = -70.0306493510356

x6 = -18.7179693424023

x7 = -98.3049832333437

x8 = -87.8330077213777

x9 = 78.6714029188813

x10 = 6782.8301256795

x11 = 62.9634396509323

x12 = -67.9362542486424

x13 = 88.0961808796507

x14 = 34.6891057686242

x15 = -61.6530689414628

x16 = -19.7651668935989

x17 = 30.5003155638378

x18 = 22.122735154265

x19 = 42.0194886270004

x20 = 60.8690445485391

x21 = -63.747464043856

x22 = 54.5858592413596

x23 = 24.2171302566582

x24 = -41.7563154687274

x25 = 68.1994274069153

x26 = 70.2938225093085

x27 = -26.0483522007785

x28 = 44.1138837293936

x29 = 43.066686178197

x30 = -21.8595619959921

x31 = 82.8601931236677

x32 = -65.8418591462492

x33 = -9.29319138163291

x34 = 95.4265637380269

x35 = -54.3226860830866

x36 = -1.96280852325673

x37 = 12.6979571934956

x38 = -85.7386126189845

x39 = -3.01000607445333

x40 = 80.7657980212745

x41 = -71.0778469022322

x42 = 57.7274518949493

x43 = 100.66255149401

x44 = 10.6035620911024

x45 = -37.5675252639411

x46 = -43.8507105711206

x47 = 0.131586579136467

x48 = 40.9722910758038

x49 = -45.9451056735138

x50 = 75.5298102652915

x51 = -31.2843399567615

x52 = 50.3970690365732

x53 = -92.0217979261641

x54 = -78.4082297606084

x55 = 48.30267393418

x56 = -60.6058713902662

x57 = -75.2666371070186

x58 = 64.0106372021289

x59 = 16.886747398282

x60 = -23.9539570983853

x61 = -17.6707717912057

x62 = -53.27548853189

x63 = -27.0955497519751

x64 = 94.3793661868303

x65 = 20.0283400518718

x66 = -49.0866983271036

x67 = 38.8778959734106

x68 = 26.3115253590514

x69 = 46.2082788317868

x70 = 92.2849710844371

x71 = -81.5498224141982

x72 = -48.039500775907

x73 = 32.594710666231

x74 = 86.0017857772575

x75 = -83.6442175165914

x76 = 8.50916698870925

x77 = 56.6802543437527

x78 = 4.32037678392286

x79 = -5.10440117684652

x80 = -93.0689954773607

x81 = 73.4354151628983

x82 = 2.22598168152966

x83 = 90.1905759820439

x84 = -89.9274028237709

x85 = -39.6619203663343

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