1+ctg4x=0 (уравнение)

Найду корень уравнения: 1+ctg4x=0

Вы ввели

1 + cot(4*x) = 0

$$\cot{\left(4 x \right)} + 1 = 0$$

Подробное решение

Дано уравнение
$$\cot{\left(4 x \right)} + 1 = 0$$
преобразуем
$$\cot{\left(4 x \right)} + 1 = 0$$
$$\left(\cot{\left(4 x \right)} + 1\right) + 0 = 0$$
Сделаем замену
$$w = \cot{\left(4 x \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = -1$$
Получим ответ: w = -1
делаем обратную замену
$$\cot{\left(4 x \right)} = w$$
подставляем w:

Быстрый ответ

     -pi 
x1 = ----
      16 

$$x_{1} = - \frac{\pi}{16}$$

Сумма и произведение корней

сумма

    pi
0 - --
    16

$$- \frac{\pi}{16} + 0$$

=

-pi 
----
 16 

$$- \frac{\pi}{16}$$

произведение

  -pi 
1*----
   16 

$$1 \left(- \frac{\pi}{16}\right)$$

=

-pi 
----
 16 

$$- \frac{\pi}{16}$$

Численный ответ

x1 = 40.644354955818

x2 = -9.62112750161874

x3 = 100.334615374024

x4 = 62.6355035309465

x5 = 44.5713457728052

x6 = 96.4076245570368

x7 = -49.6764338348886

x8 = -31.6122760767473

x9 = -21.4020999525805

x10 = 35.9319659754333

x11 = 94.0514300668444

x12 = 6.08683576633022

x13 = 4.51603943953533

x14 = -37.8954613839269

x15 = -3.33794219443916

x16 = 32.004975158446

x17 = 53.9961237335746

x18 = -52.0326283250809

x19 = -27.6852852597601

x20 = -74.0237769002095

x21 = 10.0138265833175

x22 = -91.3025364949534

x23 = -8.05033117482385

x24 = 97.9784208838317

x25 = 26.5071880146639

x26 = 16.2970118904971

x27 = -65.3843971028376

x28 = 56.3523182237669

x29 = -59.8866099590554

x30 = 50.0691329165873

x31 = -96.0149254753381

x32 = -55.9596191420682

x33 = 12.3700210735098

x34 = 64.2062998577414

x35 = 75.9872723087031

x36 = 92.4806337400495

x37 = -93.6587309851457

x38 = -53.6034246518758

x39 = -75.5945732270044

x40 = -45.7494430179014

x41 = 84.6266521060751

x42 = 42.2151512826128

x43 = 82.2704576158827

x44 = -85.8047493511712

x45 = -57.5304154688631

x46 = -69.3113879198248

x47 = 18.6532063806894

x48 = -89.7317401681585

x49 = -15.9043128087983

x50 = 34.3611696486384

x51 = 8.44303025652257

x52 = 2.15984494934298

x53 = -35.5392668937345

x54 = -61.4574062858503

x55 = -23.7582944427728

x56 = 46.1421420996001

x57 = 48.4983365897924

x58 = -17.4751091355932

x59 = -79.5215640439916

x60 = -30.0414797499524

x61 = -25.3290907695677

x62 = -13.548118318606

x63 = -71.6675824100172

x64 = 70.489485164921

x65 = -43.393248527709

x66 = 74.4164759819082

x67 = -77.9507677171967

x68 = -87.3755456779661

x69 = -47.3202393446963

x70 = -33.9684705669396

x71 = -97.585721802133

x72 = 66.5624943479338

x73 = 78.3434667988955

x74 = -67.7405915930299

x75 = -81.877758534184

x76 = 38.2881604656256

x77 = 88.5536429230623

x78 = 28.0779843414588

x79 = -11.9773219918111

x80 = -99.9419162923253

x81 = -19.8313036257856

x82 = 58.7085127139593

x83 = 30.4341788316511

x84 = 52.4253274067797

x85 = -39.4662577107218

x86 = 20.2240027074843

x87 = 24.1509935244715

x88 = 72.0602814917159

x89 = 60.2793090407542

x90 = -41.8224522009141

x91 = 90.1244392498572

x92 = 13.9408174003047

x93 = 68.1332906747286

x94 = 80.6996612890878

x95 = 22.5801971976766

x96 = -1.76714586764426

x97 = -63.8136007760427

x98 = 86.1974484328699

x99 = -5.6941366846315

x100 = -83.4485548609789

График