sin(x^2)=0 (уравнение)

Найду корень уравнения: sin(x^2)=0

Вы ввели

   / 2\    
sin\x / = 0

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

Подробное решение

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

        ____
x2 = -\/ pi 

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

       ____
x3 = \/ pi 

$$x_{3} = \sqrt{\pi}$$

Сумма и произведение корней

сумма

          ____     ____
0 + 0 - \/ pi  + \/ pi 

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

=

0

$$0$$

произведение

       ____   ____
1*0*-\/ pi *\/ pi 

$$\sqrt{\pi} 1 \cdot 0 \left(- \sqrt{\pi}\right)$$

=

0

$$0$$

Численный ответ

x1 = -1.77245385090552

x2 = 42.2424505354389

x3 = 86.2148955714351

x4 = 82.1853040708499

x5 = -65.7004437278195

x6 = -43.5966002736661

x7 = -43.8480866628973

x8 = -55.8533929588406

x9 = -5.87856438167413

x10 = 16.244807875181

x11 = -13.6144763601762

x12 = -509.434811845833

x13 = 5.60499121639793

x14 = -44.5587988737213

x15 = 1523.05464995283

x16 = 94.1238082693386

x17 = -7.72594721818665

x18 = 83.568896540101

x19 = -64.1275664870346

x20 = -95.8600986425016

x21 = 84.7262604713124

x22 = 66.2243410266297

x23 = 70.4759390524558

x24 = -47.3281688005095

x25 = -93.8731452190634

x26 = 23.7138163312566

x27 = 8.1224039375905

x28 = 0.0

x29 = -19.8166364880301

x30 = 60.0806953935677

x31 = -67.5860615683408

x32 = 6.13996024767893

x33 = -11.6227571644753

x34 = 32.6343363586107

x35 = -3.96332729760601

x36 = 64.2499240996983

x37 = -30.2357976940353

x38 = -79.405141242584

x39 = 53.8779325133859

x40 = 96.2035963853511

x41 = 22.137941502317

x42 = -41.8314129339366

x43 = 97.6620463450291

x44 = -86.2331131935235

x45 = -15.7539144225679

x46 = -25.6240680728152

x47 = -219.061242084455

x48 = 18.2485292908913

x49 = -30.9037888727466

x50 = -39.7914902637393

x51 = 56.3015718028556

x52 = -33.862683274665

x53 = -102.358250765251

x54 = -22.2793994368607

x55 = -50.3514177699791

x56 = -59.4499094640902

x57 = -53.9070793548543

x58 = 28.2482660354898

x59 = 30.3395228621317

x60 = 9.86860538583257

x61 = 56.6908218728778

x62 = 46.1519210773927

x63 = 25.8681123241458

x64 = 105.367871942952

x65 = 78.2292943160867

x66 = -89.7498945058111

x67 = 80.212104788192

x68 = -60.9888981852461

x69 = -9.86860538583257

x70 = -67.446468865301

x71 = 3.96332729760601

x72 = 52.2498231190263

График