-2ctg3x=2 (уравнение)

Найду корень уравнения: -2ctg3x=2

Вы ввели

-2*cot(3*x) = 2

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

Подробное решение

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

w = 2 / (-2)

Получим ответ: w = -1
делаем обратную замену
$$\cot{\left(3 x \right)} = w$$
подставляем w:

Быстрый ответ

     -pi 
x1 = ----
      12 

$$x_{1} = - \frac{\pi}{12}$$

Сумма и произведение корней

сумма

-pi 
----
 12 

$$- \frac{\pi}{12}$$

=

-pi 
----
 12 

$$- \frac{\pi}{12}$$

произведение

-pi 
----
 12 

$$- \frac{\pi}{12}$$

=

-pi 
----
 12 

$$- \frac{\pi}{12}$$

Численный ответ

x1 = 3.92699081698724

x2 = 82.4668071567321

x3 = -84.037603483527

x4 = -77.7544181763474

x5 = -11.7809724509617

x6 = -15.9697626557481

x7 = 80.3724120543389

x8 = -7.59218224617533

x9 = 90.8443875663049

x10 = -73.565627971561

x11 = 42.6733002112614

x12 = -45.2912940892529

x13 = -71.4712328691678

x14 = -67.2824426643814

x15 = -1.30899693899575

x16 = -81.9432083811338

x17 = -23.3001455141243

x18 = 2.87979326579064

x19 = -21.2057504117311

x20 = 12.30457122656

x21 = -97.6511716490827

x22 = 6.02138591938044

x23 = 18.5877565337396

x24 = -91.3679863419031

x25 = 8.11578102177363

x26 = 24.8709418409192

x27 = -89.27359123951

x28 = -49.4800842940392

x29 = 47.9092879672443

x30 = -99.7455667514759

x31 = -25.3945406165175

x32 = -37.9609112308767

x33 = -47.3856891916461

x34 = 20.6821516361328

x35 = 69.9004365423729

x36 = -35.8665161284835

x37 = -13.8753675533549

x38 = 66.7588438887831

x39 = 44.7676953136546

x40 = 93.9859802198946

x41 = -69.3768377667746

x42 = 98.174770424681

x43 = 54.1924732744239

x44 = -31.6777259236971

x45 = 25.9181393921158

x46 = -75.6600230739542

x47 = 40.5789051088682

x48 = 46.8620904160477

x49 = -27.4889357189107

x50 = -33.7721210260903

x51 = 22.776546738526

x52 = 16.4933614313464

x53 = -18.0641577581413

x54 = 96.0803753222878

x55 = -3.40339204138894

x56 = -41.1025038844665

x57 = -19.1113553093379

x58 = 60.4756585816035

x59 = 78.2780169519457

x60 = 32.2013246992954

x61 = 50.0036830696375

x62 = -93.4623814442964

x63 = 74.0892267471593

x64 = 28.012534494509

x65 = -29.5833308213039

x66 = 10.2101761241668

x67 = -65.1880475619882

x68 = 52.0980781720307

x69 = 68.8532389911763

x70 = 88.7499924639117

x71 = -87.1791961371168

x72 = 76.1836218495525

x73 = 14.3989663289532

x74 = 56.2868683768171

x75 = 100.269165527074

x76 = 36.3901149040818

x77 = 30.1069295969022

x78 = -55.7632696012188

x79 = -5.49778714378214

x80 = 71.9948316447661

x81 = -59.9520598060052

x82 = -86.1319985859202

x83 = 86.6555973615185

x84 = -79.8488132787406

x85 = 62.5700536839967

x86 = 64.6644487863899

x87 = 34.2957198016886

x88 = 58.3812634792103

x89 = -63.093652459595

x90 = -40.0553063332699

x91 = -95.5567765466895

x92 = -62.0464549083984

x93 = -9.68657734856853

x94 = 91.8915851175014

x95 = -43.1968989868597

x96 = -57.857664703612

x97 = -51.5744793964324

x98 = 38.484510006475

x99 = 84.5612022591253

x100 = -53.6688744988256

График