Квадратные уравнения Вариант 1 Решите уравнения: 2 1. x²-4x-45 = 0; 2 2. 4 + 8x-5x² = 0; 3. 3x²-5x + 7 = 1 + 3x + x²; 4. (x+2)(2x-8)-14 = 0; 5. 2(x+4)(x+2) = x² + 2x.

Решим данные квадратные уравнения.

1. x² - 4x - 45 = 0

   D = (-4)² - 4 × 1 × (-45) = 16 + 180 = 196

   x₁ = (4 + √196) / 2 = (4 + 14) / 2 = 18 / 2 = 9

   x₂ = (4 - √196) / 2 = (4 - 14) / 2 = -10 / 2 = -5

   Ответ: x₁ = 9; x₂ = -5

2. 4 + 8x - 5x² = 0

   -5x² + 8x + 4 = 0

   D = 8² - 4 × (-5) × 4 = 64 + 80 = 144

   x₁ = (-8 + √144) / (2 × (-5)) = (-8 + 12) / (-10) = 4 / (-10) = -0.4

   x₂ = (-8 - √144) / (2 × (-5)) = (-8 - 12) / (-10) = -20 / (-10) = 2

   Ответ: x₁ = -0.4; x₂ = 2

3. 3x² - 5x + 7 = 1 + 3x + x²

   2x² - 8x + 6 = 0

   x² - 4x + 3 = 0

   D = (-4)² - 4 × 1 × 3 = 16 - 12 = 4

   x₁ = (4 + √4) / 2 = (4 + 2) / 2 = 6 / 2 = 3

   x₂ = (4 - √4) / 2 = (4 - 2) / 2 = 2 / 2 = 1

   Ответ: x₁ = 3; x₂ = 1

4. (x + 2)(2x - 8) - 14 = 0

   2x² - 8x + 4x - 16 - 14 = 0

   2x² - 4x - 30 = 0

   x² - 2x - 15 = 0

   D = (-2)² - 4 × 1 × (-15) = 4 + 60 = 64

   x₁ = (2 + √64) / 2 = (2 + 8) / 2 = 10 / 2 = 5

   x₂ = (2 - √64) / 2 = (2 - 8) / 2 = -6 / 2 = -3

   Ответ: x₁ = 5; x₂ = -3

5. 2(x + 4)(x + 2) = x² + 2x

   2(x² + 2x + 4x + 8) = x² + 2x

   2x² + 12x + 16 = x² + 2x

   x² + 10x + 16 = 0

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

   x₁ = (-10 + √36) / 2 = (-10 + 6) / 2 = -4 / 2 = -2

   x₂ = (-10 - √36) / 2 = (-10 - 6) / 2 = -16 / 2 = -8

   Ответ: x₁ = -2; x₂ = -8