cos(x^2)=0 (уравнение)

Найду корень уравнения: cos(x^2)=0

Вы ввели

   / 2\    
cos\x / = 0

$$\cos{\left(x^{2} \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(x^{2} \right)} = 0$$
преобразуем
$$\cos{\left(x^{2} \right)} - 1 = 0$$
$$\cos{\left(x^{2} \right)} - 1 = 0$$
Сделаем замену
$$w = \cos{\left(x^{2} \right)}$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = 1$$
Получим ответ: w = 1
делаем обратную замену
$$\cos{\left(x^{2} \right)} = w$$
подставляем w:

Быстрый ответ

        ___   ____ 
     -\/ 2 *\/ pi  
x1 = --------------
           2       

$$x_{1} = - \frac{\sqrt{2} \sqrt{\pi}}{2}$$

       ___   ____
     \/ 2 *\/ pi 
x2 = ------------
          2      

$$x_{2} = \frac{\sqrt{2} \sqrt{\pi}}{2}$$

        ___   ____ 
     -\/ 6 *\/ pi  
x3 = --------------
           2       

$$x_{3} = - \frac{\sqrt{6} \sqrt{\pi}}{2}$$

       ___   ____
     \/ 6 *\/ pi 
x4 = ------------
          2      

$$x_{4} = \frac{\sqrt{6} \sqrt{\pi}}{2}$$

Сумма и произведение корней

сумма

      ___   ____     ___   ____     ___   ____     ___   ____
    \/ 2 *\/ pi    \/ 2 *\/ pi    \/ 6 *\/ pi    \/ 6 *\/ pi 
0 - ------------ + ------------ - ------------ + ------------
         2              2              2              2      

$$\left(- \frac{\sqrt{6} \sqrt{\pi}}{2} + \left(\left(- \frac{\sqrt{2} \sqrt{\pi}}{2} + 0\right) + \frac{\sqrt{2} \sqrt{\pi}}{2}\right)\right) + \frac{\sqrt{6} \sqrt{\pi}}{2}$$

=

0

$$0$$

произведение

     ___   ____    ___   ____    ___   ____    ___   ____
  -\/ 2 *\/ pi   \/ 2 *\/ pi  -\/ 6 *\/ pi   \/ 6 *\/ pi 
1*--------------*------------*--------------*------------
        2             2             2             2      

$$\frac{\sqrt{6} \sqrt{\pi}}{2} - \frac{\sqrt{6} \sqrt{\pi}}{2} \frac{\sqrt{2} \sqrt{\pi}}{2} \cdot 1 \left(- \frac{\sqrt{2} \sqrt{\pi}}{2}\right)$$

=

    2
3*pi 
-----
  4  

$$\frac{3 \pi^{2}}{4}$$

Численный ответ

x1 = -21.7441875995693

x2 = -47.8726627710821

x3 = 18.1189522958733

x4 = -85.7673550856064

x5 = 62.2255007657586

x6 = -92.1420324625326

x7 = -89.407955502065

x8 = -79.6323098451313

x9 = -29.8962056111858

x10 = 103.115082970798

x11 = -13.7864555104705

x12 = -42.0000508927152

x13 = -8.7731989612085

x14 = 89.4957567168811

x15 = 56.1199308198413

x16 = 17.4115964538412

x17 = 20.2479095536667

x18 = 68.1530977897007

x19 = -81.792551958106

x20 = 32.1249620498491

x21 = -58.8524077721783

x22 = -93.7978156802077

x23 = -69.7703218907394

x24 = -65.8556653468835

x25 = 16.0012437412711

x26 = 6.2665706865775

x27 = -57.7477324384739

x28 = 34.2088185043301

x29 = 22.3146238057912

x30 = -7.82694427889971

x31 = 40.1647585280723

x32 = 57.4750787320006

x33 = 26.0797777885892

x34 = -3.31595752197827

x35 = 4.15677273792348

x36 = -33.7930307841704

x37 = -22.2441192889355

x38 = -97.7504683154682

x39 = 36.042316272118

x40 = -16.0012437412711

x41 = 31.3829459563694

x42 = 10.2588183479024

x43 = -75.8953893880049

x44 = -46.338737344997

x45 = 23.3466555505886

x46 = 92.0738169932802

x47 = 84.0842093790732

x48 = 60.2503967723284

x49 = 23.5476347720657

x50 = -3.7599424119465

x51 = -2.1708037636748

x52 = 2.1708037636748

x53 = 66.1412713071331

x54 = -60.5883736018691

x55 = -5.16754657023168

x56 = -67.8759576469418

x57 = -43.9375543883695

x58 = 67.736962365963

x59 = -76.1639733394572

x60 = 96.1791015163645

x61 = 114.587462209783

x62 = 46.0326432528734

x63 = -32.0270198644374

x64 = 70.1296178457777

x65 = 82.2330723422884

x66 = -63.2520216621303

x67 = -68.2222069145618

x68 = -53.6295447898027

x69 = 80.1827248574873

x70 = 13.5566651590649

x71 = 27.9969170993996

x72 = -50.6779241318116

x73 = 54.1251803643413

x74 = -17.8569777493103

x75 = -71.6803654074538

x76 = 36.7757479512029

x77 = 63.9435910678085

x78 = 58.181320750246

x79 = 41.9626343588803

x80 = -37.7869535826396

x81 = -74.2423350301113

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