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4cos^2x-2cosx=0

4cos^2x-2cosx=0 уравнение

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Численное решение:

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Решение

Вы ввели [src]
     2                  
4*cos (x) - 2*cos(x) = 0
$$4 \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} = 0$$
График
Быстрый ответ [src]
      pi
x_1 = --
      3 
$$x_{1} = \frac{\pi}{3}$$
      pi
x_2 = --
      2 
$$x_{2} = \frac{\pi}{2}$$
      3*pi
x_3 = ----
       2  
$$x_{3} = \frac{3 \pi}{2}$$
      5*pi
x_4 = ----
       3  
$$x_{4} = \frac{5 \pi}{3}$$
Сумма и произведение корней [src]
сумма
pi   pi   3*pi   5*pi
-- + -- + ---- + ----
3    2     2      3  
$$\left(\frac{\pi}{3}\right) + \left(\frac{\pi}{2}\right) + \left(\frac{3 \pi}{2}\right) + \left(\frac{5 \pi}{3}\right)$$
=
4*pi
$$4 \pi$$
произведение
pi   pi   3*pi   5*pi
-- * -- * ---- * ----
3    2     2      3  
$$\left(\frac{\pi}{3}\right) * \left(\frac{\pi}{2}\right) * \left(\frac{3 \pi}{2}\right) * \left(\frac{5 \pi}{3}\right)$$
=
    4
5*pi 
-----
  12 
$$\frac{5 \pi^{4}}{12}$$
Численный ответ [src]
x1 = 68.0678408277789
x2 = -20.4203522483337
x3 = -32.4631240870945
x4 = 70.162235930172
x5 = -80.1106126665397
x6 = -54.9778714378214
x7 = -7.85398163397448
x8 = -26.1799387799149
x9 = 80.634211442138
x10 = -83.2522053201295
x11 = 83.2522053201295
x12 = -29.845130209103
x13 = 48.6946861306418
x14 = -1.5707963267949
x15 = 86.3937979737193
x16 = -4.71238898038469
x17 = 10.9955742875643
x18 = -98.9601685880785
x19 = -92.6769832808989
x20 = 24.0855436775217
x21 = -45.0294947014537
x22 = 17.8023583703422
x23 = 36.1283155162826
x24 = -49.2182849062401
x25 = 58.1194640914112
x26 = -70.162235930172
x27 = 45.553093477052
x28 = 26.1799387799149
x29 = 55.5014702134197
x30 = -76.9690200129499
x31 = -36.1283155162826
x32 = 76.9690200129499
x33 = 54.9778714378214
x34 = 76.4454212373516
x35 = 14.1371669411541
x36 = 38.7463093942741
x37 = -39.2699081698724
x38 = -64.4026493985908
x39 = 32.4631240870945
x40 = -164.410015537866
x41 = -93.2005820564972
x42 = 95.8185759344887
x43 = -24.0855436775217
x44 = -42.4115008234622
x45 = 51.8362787842316
x46 = -68.0678408277789
x47 = -63.8790506229925
x48 = -61.7846555205993
x49 = 17.2787595947439
x50 = -17.8023583703422
x51 = 32.9867228626928
x52 = -95.8185759344887
x53 = 39.2699081698724
x54 = 67.5442420521806
x55 = -26.7035375555132
x56 = 61.261056745001
x57 = -48.6946861306418
x58 = -10.9955742875643
x59 = -5.23598775598299
x60 = 30.3687289847013
x61 = 4.71238898038469
x62 = 19.8967534727354
x63 = -14.1371669411541
x64 = -76.4454212373516
x65 = 92.6769832808989
x66 = -99.4837673636768
x67 = 89.5353906273091
x68 = -51.8362787842316
x69 = -58.1194640914112
x70 = 63.8790506229925
x71 = 61.7846555205993
x72 = -13.6135681655558
x73 = -86.3937979737193
x74 = -19830.78002701
x75 = 82.7286065445312
x76 = 26.7035375555132
x77 = 11.5191730631626
x78 = -55.5014702134197
x79 = -45.553093477052
x80 = 1.5707963267949
x81 = -11.5191730631626
x82 = 7.85398163397448
x83 = -312.588469032184
x84 = 98.9601685880785
x85 = -1.0471975511966
x86 = -89.5353906273091
x87 = 99.4837673636768
x88 = -73.8274273593601
x89 = -36.6519142918809
x90 = 74.3510261349584
x91 = 80.1106126665397
x92 = -32.9867228626928
x93 = 42.4115008234622
x94 = -19.8967534727354
x94 = -19.8967534727354
График
4cos^2x-2cosx=0 уравнение