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cos^2x=cosx+2

cos^2x=cosx+2 уравнение

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Численное решение:

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Решение

Вы ввели [src]
   2                
cos (x) = cos(x) + 2
$$\cos^{2}{\left(x \right)} = \cos{\left(x \right)} + 2$$
График
Быстрый ответ [src]
x_1 = pi
$$x_{1} = \pi$$
x_2 = 2*pi - I*im(acos(2))
$$x_{2} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}$$
x_3 = I*im(acos(2))
$$x_{3} = i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}$$
Сумма и произведение корней [src]
сумма
pi + 2*pi - I*im(acos(2)) + I*im(acos(2))
$$\left(\pi\right) + \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right) + \left(i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right)$$
=
3*pi
$$3 \pi$$
произведение
pi * 2*pi - I*im(acos(2)) * I*im(acos(2))
$$\left(\pi\right) * \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right) * \left(i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right)$$
=
pi*(2*pi*I + im(acos(2)))*im(acos(2))
$$\pi \left(\operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)} + 2 i \pi\right) \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}$$
Численный ответ [src]
x1 = 78.5398156663698
x2 = -3.14159291704141
x3 = -91.1061867148735
x4 = -2315.35378614432
x5 = -72.256630304071
x6 = 15.7079634444905
x7 = -47.1238895758347
x8 = 21.9911485851996
x9 = -53.4070755045829
x10 = -15.7079632965508
x11 = -9.42477844645654
x12 = -78.5398164880203
x13 = 78.539816185312
x14 = -65.9734457649873
x15 = 3.14159235765986
x16 = -9.42477813010624
x17 = 9.42477823100035
x18 = -3.14159243826294
x19 = 78.5398169309716
x20 = -28.2743337132931
x21 = -72.2566308712826
x22 = 28.2743338651939
x23 = -21.9911485864482
x24 = 59.6902606020742
x25 = -78.5398160783629
x26 = -40.8407041932212
x27 = 4702.96420220656
x28 = 91.1061866574186
x29 = -40.8407047915367
x30 = -34.5575193582001
x31 = -97.3893724448811
x32 = 34.5575186075839
x33 = 53.4070753853423
x34 = 84.8230013925009
x35 = 91.106187255292
x36 = 40.8407042376183
x37 = 84.8230018316838
x38 = 9.42477777405166
x39 = -97.3893725703384
x40 = -47.1238900714713
x41 = -84.8230013435225
x42 = 72.2566310277185
x43 = 53.4070749084384
x44 = 47.123890106208
x45 = 40.840704697651
x46 = -34.5575189235698
x47 = 65.9734457529257
x48 = 47.1238895073209
x49 = 97.3893720447063
x50 = 97.3893725394505
x51 = 59.6902609894284
x52 = 4143.76071021141
x53 = 3422008.07225648
x54 = 34.5575190275229
x55 = -53.4070752875747
x56 = 15.7079639324176
x57 = -91.106187225664
x58 = -59.6902604576945
x59 = -84.8230019402376
x60 = -28.2743331480093
x61 = 3.14159295669587
x61 = 3.14159295669587
График
cos^2x=cosx+2 уравнение