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4sin^2(2x)=3

4sin^2(2x)=3 уравнение

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Численное решение:

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Решение

Вы ввели [src]
     2         
4*sin (2*x) = 3
$$4 \sin^{2}{\left(2 x \right)} = 3$$
График
Сумма и произведение корней [src]
сумма
-pi    pi   pi   2*pi
---- + -- + -- + ----
 6     6    3     3  
$$\left(- \frac{\pi}{6}\right) + \left(\frac{\pi}{6}\right) + \left(\frac{\pi}{3}\right) + \left(\frac{2 \pi}{3}\right)$$
=
pi
$$\pi$$
произведение
-pi    pi   pi   2*pi
---- * -- * -- * ----
 6     6    3     3  
$$\left(- \frac{\pi}{6}\right) * \left(\frac{\pi}{6}\right) * \left(\frac{\pi}{3}\right) * \left(\frac{2 \pi}{3}\right)$$
=
   4 
-pi  
-----
 162 
$$- \frac{\pi^{4}}{162}$$
Быстрый ответ [src]
      -pi 
x_1 = ----
       6  
$$x_{1} = - \frac{\pi}{6}$$
      pi
x_2 = --
      6 
$$x_{2} = \frac{\pi}{6}$$
      pi
x_3 = --
      3 
$$x_{3} = \frac{\pi}{3}$$
      2*pi
x_4 = ----
       3  
$$x_{4} = \frac{2 \pi}{3}$$
Численный ответ [src]
x1 = -78.0162175641465
x2 = -61.7846555205993
x3 = -100.007366139275
x4 = 24.0855436775217
x5 = 82.2050077689329
x6 = 56.025068989018
x7 = -92.1533845053006
x8 = -47.6474885794452
x9 = 62.3082542961976
x10 = -24.0855436775217
x11 = 2.0943951023932
x12 = 44.5058959258554
x13 = -86.9173967493176
x14 = -68.0678408277789
x15 = 26.1799387799149
x16 = -60.2138591938044
x17 = 34.0339204138894
x18 = 19.8967534727354
x19 = 84.2994028713261
x20 = 41.8879020478639
x21 = 49.7418836818384
x22 = 88.4881930761125
x23 = 48.1710873550435
x24 = -12.0427718387609
x25 = -49.7418836818384
x26 = -27.7507351067098
x27 = -53.9306738866248
x28 = -39.7935069454707
x29 = -34.0339204138894
x30 = -25.6563400043166
x31 = 93.7241808320955
x32 = -41.8879020478639
x33 = -46.0766922526503
x34 = -3.66519142918809
x35 = 22.5147473507269
x36 = 92.1533845053006
x37 = 18.3259571459405
x38 = 70.162235930172
x39 = 9.94837673636768
x40 = -93.7241808320955
x41 = -63.8790506229925
x42 = -79.0634151153431
x43 = -5.75958653158129
x44 = 85.870199198121
x45 = 30.3687289847013
x46 = -42.9350995990605
x47 = 71.733032256967
x48 = -97.9129710368819
x49 = 53.9306738866248
x50 = -82.2050077689329
x51 = -79.5870138909414
x52 = 63.8790506229925
x53 = 100.007366139275
x54 = -17.8023583703422
x55 = -83.7758040957278
x56 = 0.523598775598299
x57 = -93.2005820564972
x58 = 12.0427718387609
x59 = -69.6386371545737
x60 = -9.94837673636768
x61 = -75.9218224617533
x62 = 8.37758040957278
x63 = 68.0678408277789
x64 = 5.75958653158129
x65 = 43.4586983746588
x66 = -2.0943951023932
x67 = 74.3510261349584
x68 = 75.9218224617533
x69 = 97.9129710368819
x70 = -71.733032256967
x71 = 60.2138591938044
x72 = -85.870199198121
x73 = -19.8967534727354
x74 = 16.2315620435473
x75 = 46.0766922526503
x76 = 4.18879020478639
x77 = -64.9262481741891
x78 = -35.6047167406843
x79 = 38.2227106186758
x80 = -16.2315620435473
x81 = 27.7507351067098
x82 = 96.342174710087
x83 = 31.9395253114962
x84 = -56.025068989018
x85 = -31.9395253114962
x86 = -90.0589894029074
x87 = -38.2227106186758
x88 = 66.497044500984
x89 = 40.317105721069
x90 = -13.6135681655558
x91 = 90.0589894029074
x92 = -57.5958653158129
x93 = 52.3598775598299
x94 = 78.0162175641465
x94 = 78.0162175641465
График
4sin^2(2x)=3 уравнение