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√2*cos^2(x)+cos(x)=0

√2*cos^2(x)+cos(x)=0 уравнение

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Численное решение:

Искать численное решение на промежутке [, ]

Решение

Вы ввели [src]
  ___    2                
\/ 2 *cos (x) + cos(x) = 0
$$\sqrt{2} \cos^{2}{\left(x \right)} + \cos{\left(x \right)} = 0$$
График
Сумма и произведение корней [src]
сумма
pi   3*pi   5*pi   3*pi
-- + ---- + ---- + ----
2     4      4      2  
$$\left(\frac{\pi}{2}\right) + \left(\frac{3 \pi}{4}\right) + \left(\frac{5 \pi}{4}\right) + \left(\frac{3 \pi}{2}\right)$$
=
4*pi
$$4 \pi$$
произведение
pi   3*pi   5*pi   3*pi
-- * ---- * ---- * ----
2     4      4      2  
$$\left(\frac{\pi}{2}\right) * \left(\frac{3 \pi}{4}\right) * \left(\frac{5 \pi}{4}\right) * \left(\frac{3 \pi}{2}\right)$$
=
     4
45*pi 
------
  64  
$$\frac{45 \pi^{4}}{64}$$
Быстрый ответ [src]
      pi
x_1 = --
      2 
$$x_{1} = \frac{\pi}{2}$$
      3*pi
x_2 = ----
       4  
$$x_{2} = \frac{3 \pi}{4}$$
      5*pi
x_3 = ----
       4  
$$x_{3} = \frac{5 \pi}{4}$$
      3*pi
x_4 = ----
       2  
$$x_{4} = \frac{3 \pi}{2}$$
Численный ответ [src]
x1 = 10.2101761241668
x2 = -70.6858347057703
x3 = -20.4203522483337
x4 = 64.4026493985908
x5 = -47.9092879672443
x6 = -80.1106126665397
x7 = -54.9778714378214
x8 = -7.85398163397448
x9 = 83.2522053201295
x10 = -29.845130209103
x11 = 48.6946861306418
x12 = -1.5707963267949
x13 = 70.6858347057703
x14 = 86.3937979737193
x15 = 91.8915851175014
x16 = -4.71238898038469
x17 = -71.4712328691678
x18 = 10.9955742875643
x19 = -98.9601685880785
x20 = -10.2101761241668
x21 = 36.1283155162826
x22 = 58.1194640914112
x23 = 90.3207887907066
x24 = 33.7721210260903
x25 = -40.0553063332699
x26 = 45.553093477052
x27 = 60.4756585816035
x28 = -76.9690200129499
x29 = 76.9690200129499
x30 = -36.1283155162826
x31 = 54.9778714378214
x32 = 23.5619449019235
x33 = 14.1371669411541
x34 = -64.4026493985908
x35 = -27.4889357189107
x36 = 95.8185759344887
x37 = -41.6261026600648
x38 = 3.92699081698724
x39 = -67.5442420521806
x40 = 51.8362787842316
x41 = 17.2787595947439
x42 = -95.8185759344887
x43 = 32.9867228626928
x44 = 39.2699081698724
x45 = -3.92699081698724
x46 = -17.2787595947439
x47 = 29.845130209103
x48 = 67.5442420521806
x49 = -26.7035375555132
x50 = -77.7544181763474
x51 = -84.037603483527
x52 = 61.261056745001
x53 = -48.6946861306418
x54 = 73.8274273593601
x55 = 20.4203522483337
x56 = -10.9955742875643
x57 = -14.1371669411541
x58 = 46.3384916404494
x59 = -54.1924732744239
x60 = -8.63937979737193
x61 = -58.1194640914112
x62 = -51.8362787842316
x63 = 47.9092879672443
x64 = -33.7721210260903
x65 = -91.8915851175014
x66 = 40.0553063332699
x67 = 54.1924732744239
x68 = -23.5619449019235
x69 = -85.6083998103219
x70 = 26.7035375555132
x71 = -45.553093477052
x72 = -66.7588438887831
x73 = 2.35619449019234
x74 = 16.4933614313464
x75 = 7.85398163397448
x76 = 98.174770424681
x77 = 98.9601685880785
x78 = 77.7544181763474
x79 = -60.4756585816035
x80 = -61.261056745001
x81 = -89.5353906273091
x82 = -73.8274273593601
x83 = 84.037603483527
x84 = 80.1106126665397
x85 = -32.9867228626928
x86 = -98.174770424681
x87 = 42.4115008234622
x87 = 42.4115008234622
График
√2*cos^2(x)+cos(x)=0 уравнение