tan(2*x)+tan(x)=0 (уравнение)

Найду корень уравнения: tan(2*x)+tan(x)=0

Вы ввели

tan(2*x) + tan(x) = 0

$$\tan{\left(x \right)} + \tan{\left(2 x \right)} = 0$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     -2*pi
x2 = -----
       3  

$$x_{2} = - \frac{2 \pi}{3}$$

     -pi 
x3 = ----
      3  

$$x_{3} = - \frac{\pi}{3}$$

     pi
x4 = --
     3 

$$x_{4} = \frac{\pi}{3}$$

     2*pi
x5 = ----
      3  

$$x_{5} = \frac{2 \pi}{3}$$

x6 = pi

$$x_{6} = \pi$$

Сумма и произведение корней

сумма

  2*pi   pi   pi   2*pi     
- ---- - -- + -- + ---- + pi
   3     3    3     3       

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

=

pi

$$\pi$$

произведение

  -2*pi -pi  pi 2*pi   
0*-----*----*--*----*pi
    3    3   3   3     

$$\pi \frac{2 \pi}{3} \frac{\pi}{3} \cdot - \frac{\pi}{3} \cdot 0 \left(- \frac{2 \pi}{3}\right)$$

=

0

$$0$$

Численный ответ

x1 = 9.42477796076938

x2 = -17.8023583703422

x3 = -53.4070751110265

x4 = -43.9822971502571

x5 = 74.3510261349584

x6 = -12.5663706143592

x7 = 72.2566310325652

x8 = -74.3510261349584

x9 = 18.8495559215388

x10 = -79.5870138909414

x11 = 96.342174710087

x12 = 30.3687289847013

x13 = 24.0855436775217

x14 = -15.707963267949

x15 = 92.1533845053006

x16 = 19.8967534727354

x17 = 21.9911485751286

x18 = -52.3598775598299

x19 = -30.3687289847013

x20 = 80.634211442138

x21 = -68.0678408277789

x22 = 85.870199198121

x23 = 15.707963267949

x24 = 50.2654824574367

x25 = 26.1799387799149

x26 = 2.0943951023932

x27 = -50.2654824574367

x28 = -65.9734457253857

x29 = 31.4159265358979

x30 = 14.6607657167524

x31 = -34.5575191894877

x32 = 36.6519142918809

x33 = -24.0855436775217

x34 = 0.0

x35 = 46.0766922526503

x36 = -63.8790506229925

x37 = 65.9734457253857

x38 = -31.4159265358979

x39 = 81.6814089933346

x40 = -85.870199198121

x41 = -59.6902604182061

x42 = -91.106186954104

x43 = -6.28318530717959

x44 = 68.0678408277789

x45 = -9.42477796076938

x46 = -97.3893722612836

x47 = -28.2743338823081

x48 = -35.6047167406843

x49 = -46.0766922526503

x50 = 62.8318530717959

x51 = -2.0943951023932

x52 = -90.0589894029074

x53 = -21.9911485751286

x54 = 97.3893722612836

x55 = 52.3598775598299

x56 = -56.5486677646163

x57 = -7.33038285837618

x58 = 6.28318530717959

x59 = 84.8230016469244

x60 = -19.8967534727354

x61 = -94.2477796076938

x62 = 41.8879020478639

x63 = -81.6814089933346

x64 = 8.37758040957278

x65 = -39.7935069454707

x66 = -57.5958653158129

x67 = -69.1150383789755

x68 = 48.1710873550435

x69 = 87.9645943005142

x70 = -75.398223686155

x71 = -3.14159265358979

x72 = 37.6991118430775

x73 = -13.6135681655558

x74 = 78.5398163397448

x75 = 34.5575191894877

x76 = -72.2566310325652

x77 = 43.9822971502571

x78 = -25.1327412287183

x79 = 53.4070751110265

x80 = -61.7846555205993

x81 = -47.1238898038469

x82 = 100.530964914873

x83 = -37.6991118430775

x84 = 70.162235930172

x85 = 58.6430628670095

x86 = -41.8879020478639

x87 = 56.5486677646163

x88 = -87.9645943005142

x89 = -78.5398163397448

x90 = -83.7758040957278

x91 = 63.8790506229925

x92 = -100.530964914873

x93 = 75.398223686155

x94 = 12.5663706143592

x95 = 28.2743338823081

x96 = 90.0589894029074

x97 = 4.18879020478639

x98 = 59.6902604182061

x99 = -96.342174710087

x100 = 40.8407044966673

x101 = 94.2477796076938

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