1. x2+4x-21=0 2. x²-4x-12=0 3. x2-14x+48=0 4. x2-3x-10=0 5. x2+8x-20=0 6. x2-9x+20=0 7. x2+17x-168=0 8. x2-21x+108=0 9. x2+x-2=0 10. x2-x-2=0 11. 2x2-5x+3=0 12. 7x2+8x+1=0

Привет, мой дорогой ученик! Давай решим эти квадратные уравнения вместе, шаг за шагом. Сейчас мы разберем каждое уравнение, используя дискриминант. 1. x² + 4x - 21 = 0 * a = 1, b = 4, c = -21 * D = b² - 4ac = 4² - 4 * 1 * (-21) = 16 + 84 = 100 * x₁ = (-b + √D) / (2a) = (-4 + √100) / 2 = (-4 + 10) / 2 = 6 / 2 = 3 * x₂ = (-b - √D) / (2a) = (-4 - √100) / 2 = (-4 - 10) / 2 = -14 / 2 = -7 * Ответ: x₁ = 3, x₂ = -7 2. x² - 4x - 12 = 0 * a = 1, b = -4, c = -12 * D = b² - 4ac = (-4)² - 4 * 1 * (-12) = 16 + 48 = 64 * x₁ = (-b + √D) / (2a) = (4 + √64) / 2 = (4 + 8) / 2 = 12 / 2 = 6 * x₂ = (-b - √D) / (2a) = (4 - √64) / 2 = (4 - 8) / 2 = -4 / 2 = -2 * Ответ: x₁ = 6, x₂ = -2 3. x² - 14x + 48 = 0 * a = 1, b = -14, c = 48 * D = b² - 4ac = (-14)² - 4 * 1 * 48 = 196 - 192 = 4 * x₁ = (-b + √D) / (2a) = (14 + √4) / 2 = (14 + 2) / 2 = 16 / 2 = 8 * x₂ = (-b - √D) / (2a) = (14 - √4) / 2 = (14 - 2) / 2 = 12 / 2 = 6 * Ответ: x₁ = 8, x₂ = 6 4. x² - 3x - 10 = 0 * a = 1, b = -3, c = -10 * D = b² - 4ac = (-3)² - 4 * 1 * (-10) = 9 + 40 = 49 * x₁ = (-b + √D) / (2a) = (3 + √49) / 2 = (3 + 7) / 2 = 10 / 2 = 5 * x₂ = (-b - √D) / (2a) = (3 - √49) / 2 = (3 - 7) / 2 = -4 / 2 = -2 * Ответ: x₁ = 5, x₂ = -2 5. x² + 8x - 20 = 0 * a = 1, b = 8, c = -20 * D = b² - 4ac = 8² - 4 * 1 * (-20) = 64 + 80 = 144 * x₁ = (-b + √D) / (2a) = (-8 + √144) / 2 = (-8 + 12) / 2 = 4 / 2 = 2 * x₂ = (-b - √D) / (2a) = (-8 - √144) / 2 = (-8 - 12) / 2 = -20 / 2 = -10 * Ответ: x₁ = 2, x₂ = -10 6. x² - 9x + 20 = 0 * a = 1, b = -9, c = 20 * D = b² - 4ac = (-9)² - 4 * 1 * 20 = 81 - 80 = 1 * x₁ = (-b + √D) / (2a) = (9 + √1) / 2 = (9 + 1) / 2 = 10 / 2 = 5 * x₂ = (-b - √D) / (2a) = (9 - √1) / 2 = (9 - 1) / 2 = 8 / 2 = 4 * Ответ: x₁ = 5, x₂ = 4 7. x² + 17x - 168 = 0 * a = 1, b = 17, c = -168 * D = b² - 4ac = 17² - 4 * 1 * (-168) = 289 + 672 = 961 * x₁ = (-b + √D) / (2a) = (-17 + √961) / 2 = (-17 + 31) / 2 = 14 / 2 = 7 * x₂ = (-b - √D) / (2a) = (-17 - √961) / 2 = (-17 - 31) / 2 = -48 / 2 = -24 * Ответ: x₁ = 7, x₂ = -24 8. x² - 21x + 108 = 0 * a = 1, b = -21, c = 108 * D = b² - 4ac = (-21)² - 4 * 1 * 108 = 441 - 432 = 9 * x₁ = (-b + √D) / (2a) = (21 + √9) / 2 = (21 + 3) / 2 = 24 / 2 = 12 * x₂ = (-b - √D) / (2a) = (21 - √9) / 2 = (21 - 3) / 2 = 18 / 2 = 9 * Ответ: x₁ = 12, x₂ = 9 9. x² + x - 2 = 0 * a = 1, b = 1, c = -2 * D = b² - 4ac = 1² - 4 * 1 * (-2) = 1 + 8 = 9 * x₁ = (-b + √D) / (2a) = (-1 + √9) / 2 = (-1 + 3) / 2 = 2 / 2 = 1 * x₂ = (-b - √D) / (2a) = (-1 - √9) / 2 = (-1 - 3) / 2 = -4 / 2 = -2 * Ответ: x₁ = 1, x₂ = -2 10. x² - x - 2 = 0 * a = 1, b = -1, c = -2 * D = b² - 4ac = (-1)² - 4 * 1 * (-2) = 1 + 8 = 9 * x₁ = (-b + √D) / (2a) = (1 + √9) / 2 = (1 + 3) / 2 = 4 / 2 = 2 * x₂ = (-b - √D) / (2a) = (1 - √9) / 2 = (1 - 3) / 2 = -2 / 2 = -1 * Ответ: x₁ = 2, x₂ = -1 11. 2x² - 5x + 3 = 0 * a = 2, b = -5, c = 3 * D = b² - 4ac = (-5)² - 4 * 2 * 3 = 25 - 24 = 1 * x₁ = (-b + √D) / (2a) = (5 + √1) / (2 * 2) = (5 + 1) / 4 = 6 / 4 = 1.5 * x₂ = (-b - √D) / (2a) = (5 - √1) / (2 * 2) = (5 - 1) / 4 = 4 / 4 = 1 * Ответ: x₁ = 1.5, x₂ = 1 12. 7x² + 8x + 1 = 0 * a = 7, b = 8, c = 1 * D = b² - 4ac = 8² - 4 * 7 * 1 = 64 - 28 = 36 * x₁ = (-b + √D) / (2a) = (-8 + √36) / (2 * 7) = (-8 + 6) / 14 = -2 / 14 = -1 / 7 * x₂ = (-b - √D) / (2a) = (-8 - √36) / (2 * 7) = (-8 - 6) / 14 = -14 / 14 = -1 * Ответ: x₁ = -1/7, x₂ = -1

Ответ: решения уравнений выше.

Ты проделал отличную работу, решая эти уравнения! Математика может быть сложной, но с практикой ты сможешь решить любые задачи! У тебя все получится!