tan(pi×x^2) = 1 (уравнение)

Найду корень уравнения: tan(pi×x^2) = 1

Вы ввели

   /    2\    
tan\pi*x / = 1

$$\tan{\left(\pi x^{2} \right)} = 1$$

Подробное решение

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

Быстрый ответ

x1 = -1/2

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

x2 = 1/2

$$x_{2} = \frac{1}{2}$$

Численный ответ

x1 = -19.6277864263905

x2 = 32.6687924478393

x3 = 124.089685308651

x4 = 133.911351273893

x5 = -46.6931472488201

x6 = -23.1786539729985

x7 = -55.9575732139985

x8 = 86.6963090333147

x9 = 1.5

x10 = 8.5

x11 = -90.7372580586387

x12 = -24.7840674627875

x13 = 21.5928228816892

x14 = 13.7204227340122

x15 = 89.6841680565751

x16 = 64.0331945165943

x17 = -87.8649531952302

x18 = -82.3058321141339

x19 = -31.036269105677

x20 = 14.1862609591111

x21 = -6.72681202353685

x22 = -92.6997842500186

x23 = 23.6484671807709

x24 = 46.7466576345304

x25 = -5.7662812973354

x26 = -66.6051799787374

x27 = 49.6210640756524

x28 = 66.2966816665812

x29 = 42.2758796478559

x30 = -79.7762495984864

x31 = 79.9828106532897

x32 = -32.6075144713607

x33 = 79.1533322103372

x34 = 13.5

x35 = 60.730964095756

x36 = -77.7512057784315

x37 = -75.6587734502748

x38 = 23.9843699104229

x39 = -72.885183679538

x40 = -15.1079449297381

x41 = 79.1280607622858

x42 = 6.65206734782504

x43 = 92.5378301020723

x44 = 62.9305172392536

x45 = 56.9319769549592

x46 = -88.9114728255021

x47 = -9.5524865872714

x48 = -67.913547985656

x49 = 5.85234995535981

x50 = -96.655315425485

x51 = 58.8663741027082

x52 = 54.3346114369101

x53 = -22.7431308310883

x54 = 38.6425930806927

x55 = -98.3577653263839

x56 = -38.6296518234374

x57 = -10.8742815854658

x58 = -59.9520641846467

x59 = -70.1872495543172

x60 = -49.711668650328

x61 = -62.4599871918014

x62 = 4.03112887414927

x63 = -74.5268408024921

x64 = 72.0711454050787

x65 = 106.790683114212

x66 = 5.5

x67 = 125.288666686177

x68 = -152.247331667915

x69 = -25.9855729203726

x70 = 58.7813746011439

x71 = -19.2418814048939

x72 = 22.4555115728856

x73 = -8.26135582092915

x74 = 68.2440473594584

x75 = -30.7936681803256

x76 = 45.3348651701977

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