ctg(x)=sqrt(3) (уравнение)

Найду корень уравнения: ctg(x)=sqrt(3)

Вы ввели

           ___
cot(x) = \/ 3 

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

Подробное решение

Дано уравнение
$$\cot{\left(x \right)} = \sqrt{3}$$
преобразуем
$$\cot{\left(x \right)} - \sqrt{3} = 0$$
$$\cot{\left(x \right)} - \sqrt{3} = 0$$
Сделаем замену
$$w = \cot{\left(x \right)}$$
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
$$\cot{\left(x \right)} = w$$
подставляем w:

Быстрый ответ

     pi
x1 = --
     6 

$$x_{1} = \frac{\pi}{6}$$

Сумма и произведение корней

сумма

    pi
0 + --
    6 

$$0 + \frac{\pi}{6}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

произведение

  pi
1*--
  6 

$$1 \frac{\pi}{6}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

Численный ответ

x1 = 35.081117965086

x2 = -12.0427718387609

x3 = -8.90117918517108

x4 = 53.9306738866248

x5 = 6.80678408277789

x6 = 85.3466004225227

x7 = -71.733032256967

x8 = 97.9129710368819

x9 = 0.523598775598299

x10 = -40.317105721069

x11 = -93.7241808320955

x12 = 44.5058959258554

x13 = 31.9395253114962

x14 = 91.6297857297023

x15 = -43.4586983746588

x16 = -24.60914245312

x17 = 50.789081233035

x18 = -100.007366139275

x19 = -87.4409955249159

x20 = 38.2227106186758

x21 = 3.66519142918809

x22 = 57.0722665402146

x23 = 88.4881930761125

x24 = 19.3731546971371

x25 = -18.3259571459405

x26 = -37.1755130674792

x27 = -96.8657734856853

x28 = -81.1578102177363

x29 = -74.8746249105567

x30 = 66.497044500984

x31 = -2.61799387799149

x32 = -90.5825881785057

x33 = 94.7713783832921

x34 = 79.0634151153431

x35 = -59.1666616426078

x36 = -62.3082542961976

x37 = 9.94837673636768

x38 = -21.4675497995303

x39 = 25.6563400043166

x40 = -46.6002910282486

x41 = 22.5147473507269

x42 = 16.2315620435473

x43 = -15.1843644923507

x44 = 82.2050077689329

x45 = -78.0162175641465

x46 = -56.025068989018

x47 = -65.4498469497874

x48 = 69.6386371545737

x49 = 63.3554518473942

x50 = 28.7979326579064

x51 = 60.2138591938044

x52 = 13.0899693899575

x53 = -30.8923277602996

x54 = 47.6474885794452

x55 = -49.7418836818384

x56 = -27.7507351067098

x57 = -84.2994028713261

x58 = -34.0339204138894

x59 = 72.7802298081635

x60 = 75.9218224617533

x61 = -5.75958653158129

x62 = 41.3643032722656

x63 = -52.8834763354282

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