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2cos²x—cosx—1=0

2cos²x—cosx—1=0 уравнение

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Численное решение:

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Решение

Вы ввели [src]
     2                    
2*cos (x) - cos(x) - 1 = 0
$$2 \cos^{2}{\left(x \right)} - \cos{\left(x \right)} - 1 = 0$$
График
Быстрый ответ [src]
x_1 = 0
$$x_{1} = 0$$
      2*pi
x_2 = ----
       3  
$$x_{2} = \frac{2 \pi}{3}$$
      4*pi
x_3 = ----
       3  
$$x_{3} = \frac{4 \pi}{3}$$
x_4 = 2*pi
$$x_{4} = 2 \pi$$
Сумма и произведение корней [src]
сумма
    2*pi   4*pi       
0 + ---- + ---- + 2*pi
     3      3         
$$\left(0\right) + \left(\frac{2 \pi}{3}\right) + \left(\frac{4 \pi}{3}\right) + \left(2 \pi\right)$$
=
4*pi
$$4 \pi$$
произведение
    2*pi   4*pi       
0 * ---- * ---- * 2*pi
     3      3         
$$\left(0\right) * \left(\frac{2 \pi}{3}\right) * \left(\frac{4 \pi}{3}\right) * \left(2 \pi\right)$$
=
0
$$0$$
Численный ответ [src]
x1 = 87.9645943357073
x2 = 58.6430628670095
x3 = -10.471975511966
x4 = 54.4542726622231
x5 = 39.7935069454707
x6 = 14.6607657167524
x7 = -46.0766922526503
x8 = -50.2654822985064
x9 = 69.1150384283402
x10 = -77.4926187885482
x11 = 35.6047167406843
x12 = 60.7374579694027
x13 = 83.7758040957278
x14 = -90.0589894029074
x15 = 25.1327417460082
x16 = 48.1710873550435
x17 = -12.5663703884691
x18 = 94.2477796093525
x19 = 8.37758040957278
x20 = -85.870199198121
x21 = -62.8318529503654
x22 = 100.530964769014
x23 = -69.11503909537
x24 = 4.18879020478639
x25 = -33.5103216382911
x26 = 16.7551608191456
x27 = 0.0
x28 = 43.9822971694142
x29 = 75.3982239117447
x30 = 62.8318528532238
x31 = 50.2654824463501
x32 = -41.8879020478639
x33 = -18.8495558006412
x34 = -37.6991118771132
x35 = 31.4159267619367
x36 = -29.3215314335047
x37 = -83.7758040957278
x38 = 52.3598775598299
x39 = -96.342174710087
x40 = -100.530964690899
x41 = 37.6991120149696
x42 = -8.37758040957278
x43 = -31.4159267013407
x44 = 41.8879020478639
x45 = -35.6047167406843
x46 = -73.3038285837618
x47 = 25.1327411125589
x48 = -18.8495555012277
x49 = -56.5486675394273
x50 = -43.9822971745925
x51 = -18.8495558410301
x52 = 18.8495557025416
x53 = 81.6814091712551
x54 = -87.9645943588266
x55 = 43.9822969706241
x56 = -27.2271363311115
x57 = -94.2477794556977
x58 = 77.4926187885482
x59 = 85.870199198121
x60 = 90.0589894029074
x61 = -98.4365698124802
x62 = 25.1327412731354
x63 = -81.6814090379303
x64 = 10.471975511966
x65 = 69.1150383295746
x66 = -2.0943951023932
x67 = -92.1533845053006
x68 = 98.4365698124802
x69 = 6.28318528426584
x70 = 69.115037832119
x71 = 12.5663700882745
x72 = 92.1533845053006
x73 = -71.2094334813686
x74 = -6.28318514161788
x75 = 56.5486676119735
x76 = -69.1150385967809
x77 = -4.18879020478639
x78 = 33.5103216382911
x79 = -79.5870138909414
x80 = 2.0943951023932
x81 = 79.5870138909414
x82 = 25.13274122338
x83 = -62.8318529623378
x84 = -54.4542726622231
x85 = -39.7935069454707
x86 = 96.342174710087
x87 = -25.1327414474833
x88 = -52.3598775598299
x89 = -75.3982238575994
x90 = -18.8495558711096
x91 = -62.8318537995483
x92 = 12.5663704551863
x93 = -48.1710873550435
x94 = 46.0766922526503
x95 = 69.1150383780256
x95 = 69.1150383780256
График
2cos²x—cosx—1=0 уравнение