№2. Решите уравнения. 1) x² - 12x = -32 2) 11x-6+10x² = 0 3) 2(x+4)(x + 2) = x² + 2x 4) 11x+8x²-3= 3x² + 6x + 7 5) (x-5)(x-1)-21=0

№2. Решите уравнения.

1. x² - 12x = -32

   x² - 12x + 32 = 0

   D = (-12)² - 4 * 1 * 32 = 144 - 128 = 16

   x1 = (12 + \sqrt{16}) / 2 = (12 + 4) / 2 = 16 / 2 = 8

   x2 = (12 - \sqrt{16}) / 2 = (12 - 4) / 2 = 8 / 2 = 4

   Ответ: x1 = 8, x2 = 4

2. 11x-6+10x² = 0

   10x² + 11x - 6 = 0

   D = 11² - 4 * 10 * (-6) = 121 + 240 = 361

   x1 = (-11 + \sqrt{361}) / (2 * 10) = (-11 + 19) / 20 = 8 / 20 = 2/5

   x2 = (-11 - \sqrt{361}) / (2 * 10) = (-11 - 19) / 20 = -30 / 20 = -3/2

   Ответ: x1 = 2/5, x2 = -3/2

3. 2(x+4)(x + 2) = x² + 2x

   2(x² + 2x + 4x + 8) = x² + 2x

   2(x² + 6x + 8) = x² + 2x

   2x² + 12x + 16 = x² + 2x

   x² + 10x + 16 = 0

   D = 10² - 4 * 1 * 16 = 100 - 64 = 36

   x1 = (-10 + \sqrt{36}) / 2 = (-10 + 6) / 2 = -4 / 2 = -2

   x2 = (-10 - \sqrt{36}) / 2 = (-10 - 6) / 2 = -16 / 2 = -8

   Ответ: x1 = -2, x2 = -8

4. 11x+8x²-3= 3x² + 6x + 7

   5x² + 5x - 10 = 0

   x² + x - 2 = 0

   D = 1² - 4 * 1 * (-2) = 1 + 8 = 9

   x1 = (-1 + \sqrt{9}) / 2 = (-1 + 3) / 2 = 2 / 2 = 1

   x2 = (-1 - \sqrt{9}) / 2 = (-1 - 3) / 2 = -4 / 2 = -2

   Ответ: x1 = 1, x2 = -2

5. (x-5)(x-1)-21=0

   x² - x - 5x + 5 - 21 = 0

   x² - 6x - 16 = 0

   D = (-6)² - 4 * 1 * (-16) = 36 + 64 = 100

   x1 = (6 + \sqrt{100}) / 2 = (6 + 10) / 2 = 16 / 2 = 8

   x2 = (6 - \sqrt{100}) / 2 = (6 - 10) / 2 = -4 / 2 = -2

   Ответ: x1 = 8, x2 = -2