ctg3х=-√3 (уравнение)

Найду корень уравнения: ctg3х=-√3

Вы ввели

              ___
cot(3*x) = -\/ 3 

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

Подробное решение

Дано уравнение
$$\cot{\left(3 x \right)} = - \sqrt{3}$$
преобразуем
$$\cot{\left(3 x \right)} + \sqrt{3} = 0$$
$$\cot{\left(3 x \right)} + \sqrt{3} = 0$$
Сделаем замену
$$w = \cot{\left(3 x \right)}$$
Раскрываем скобочки в левой части ур-ния

w + sqrt3 = 0

Разделим обе части ур-ния на (w + sqrt(3))/w

w = 0 / ((w + sqrt(3))/w)

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

Быстрый ответ

     -pi 
x1 = ----
      18 

$$x_{1} = - \frac{\pi}{18}$$

Сумма и произведение корней

сумма

    pi
0 - --
    18

$$- \frac{\pi}{18} + 0$$

=

-pi 
----
 18 

$$- \frac{\pi}{18}$$

произведение

  -pi 
1*----
   18 

$$1 \left(- \frac{\pi}{18}\right)$$

=

-pi 
----
 18 

$$- \frac{\pi}{18}$$

Численный ответ

x1 = -5.41052068118242

x2 = 68.940505453776

x3 = -9.59931088596881

x4 = -89.1863247769102

x5 = -99.6583002888762

x6 = 46.9493568786475

x7 = 86.7428638241182

x8 = 30.1941960595019

x9 = -83.9503370209273

x10 = -59.8647933434055

x11 = -27.401669256311

x12 = -7.50491578357562

x13 = -57.7703982410123

x14 = 18.6750229963393

x15 = 96.1676417848876

x16 = -64.0535835481919

x17 = -1.22173047639603

x18 = 90.9316540289046

x19 = -31.5904594610974

x20 = -39.9680398706701

x21 = -53.5816080362259

x22 = 6.10865238198015

x23 = 64.7517152489896

x24 = -19.0240888467382

x25 = -67.1951762017817

x26 = 44.8549617762543

x27 = 62.6573201465964

x28 = -17.9768912955416

x29 = 8.20304748437335

x30 = 76.2708883121522

x31 = -21.1184839491314

x32 = 4.01425727958696

x33 = 28.0998009571087

x34 = 88.8372589265114

x35 = -91.2807198793034

x36 = 14.4862327915529

x37 = -13.7881010907552

x38 = 56.3741348394168

x39 = -23.2128790515246

x40 = 12.3918376891597

x41 = 69.9877030049726

x42 = 2.96705972839036

x43 = 82.5540736193318

x44 = -35.7792496658838

x45 = -45.2040276266531

x46 = -11.693705988362

x47 = 22.8638132011257

x48 = 42.7605666738611

x49 = -86.0447321233204

x50 = -65.1007810993885

x51 = -77.6671517137477

x52 = -42.0624349730633

x53 = 40.6661715714679

x54 = -25.3072741539178

x55 = 84.648468721725

x56 = -75.5727566113545

x57 = -95.4695100840898

x58 = -81.8559419185341

x59 = 32.2885911618951

x60 = 16.5806278939461

x61 = 66.8461103513828

x62 = 94.0732466824944

x63 = 34.3829862642883

x64 = -37.873644768277

x65 = -61.9591884457987

x66 = -97.563905186483

x67 = 74.176493209759

x68 = -15.8824961931484

x69 = 47.9965544298441

x70 = 20.7694180987325

x71 = -29.4960643587042

x72 = -43.1096325242599

x73 = 58.46852994181

x74 = 54.2797397370236

x75 = -87.091929674517

x76 = -51.4872129338327

x77 = 36.4773813666815

x78 = -47.2984227290463

x79 = 60.5629250442032

x80 = 98.2620368872808

x81 = -73.4783615089613

x82 = 72.0820981073658

x83 = -49.3928178314395

x84 = -3.31612557878923

x85 = 10.2974425867665

x86 = -55.6760031386191

x87 = -71.3839664065681

x88 = -79.7615468161409

x89 = -33.6848545634906

x90 = 50.0909495322373

x91 = 91.9788515801012

x92 = 26.0054058547155

x93 = -69.2895713041749

x94 = -93.3751149816966

x95 = 100.356431989674

x96 = 52.1853446346305

x97 = 24.9582083035189

x98 = 78.3652834145454

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