cosx+2cosx=1 (уравнение)

Найду корень уравнения: cosx+2cosx=1

Вы ввели

cos(x) + 2*cos(x) = 1

$$\cos{\left(x \right)} + 2 \cos{\left(x \right)} = 1$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} + 2 \cos{\left(x \right)} = 1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 3

Ур-ние превратится в
$$\cos{\left(x \right)} = \frac{1}{3}$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(1/3) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi$$

x2 = acos(1/3)

$$x_{2} = \operatorname{acos}{\left(\frac{1}{3} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(1/3) + 2*pi + acos(1/3)

$$\operatorname{acos}{\left(\frac{1}{3} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(1/3) + 2*pi)*acos(1/3)

$$1 \left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{3} \right)}$$

=

(-acos(1/3) + 2*pi)*acos(1/3)

$$\left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{3} \right)}$$

Численный ответ

x1 = -70.3459977963162

x2 = 64.0628124891366

x3 = -89.195553717855

x4 = 17.618596504198

x5 = 95.4787390250346

x6 = -80.4504495759938

x7 = -1.23095941734077

x8 = -74.1672642688143

x9 = 55.3177083472755

x10 = -51.4964418747775

x11 = 45.2132565675979

x12 = 36.4681524257367

x13 = -325.494676555998

x14 = 86.7336348831734

x15 = -57.7796271819571

x16 = 5.05222588983881

x17 = 80.4504495759938

x18 = -86.7336348831734

x19 = -45.2132565675979

x20 = -67.8840789616347

x21 = -61.6008936544551

x22 = -30.1849671185572

x23 = -101.761924332214

x24 = 42.7513377329163

x25 = -20.0805153388795

x26 = 93.016820190353

x27 = 23.9017818113776

x28 = -17.618596504198

x29 = 67.8840789616347

x30 = 49.0345230400959

x31 = -42.7513377329163

x32 = 57.7796271819571

x33 = 30.1849671185572

x34 = -49.0345230400959

x35 = -23.9017818113776

x36 = 26.3637006460591

x37 = -93.016820190353

x38 = 11.3354111970184

x39 = -13.7973300316999

x40 = -95.4787390250346

x41 = 13.7973300316999

x42 = -64.0628124891366

x43 = 82.9123684106754

x44 = -7.51414472452036

x45 = -36.4681524257367

x46 = -99.3000054975326

x47 = 74.1672642688143

x48 = 7.51414472452036

x49 = -76.6291831034958

x50 = 38.9300712604183

x51 = -55.3177083472755

x52 = 51.4964418747775

x53 = 76.6291831034958

x54 = -11.3354111970184

x55 = -32.6468859532387

x56 = -5.05222588983881

x57 = 1.23095941734077

x58 = -82.9123684106754

x59 = -26.3637006460591

x60 = 20.0805153388795

x61 = 32.6468859532387

x62 = 70.3459977963162

x63 = 89.195553717855

x64 = 61.6008936544551

x65 = 99.3000054975326

x66 = -38.9300712604183

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