Тренажер «Квадратные уравнения» Реши уравнения: 1. x²+5x-6=0 2. 3x²+2x-1=0 3. x²-8x-84=0 4. x²-5x+6=0 5. x²+4x+4=0 6. 2x²+3x+1=0 7. 4x²+10x-6=0 8. 3x²+32x+80=0 9. x²-2x-48 10.-x²=5x-14 11. x²+7x+2=0 12. 16x²-9=0 13. -x²+x=0 14. 3x²-12x=0 15. x²+2x=0 16. -2x²+14=0 17. 6x²=0 18. x²-64=0 19. 6x(2x+1)=5x+1 20. (x-2)²=3x-8 Вариант 1

Решим квадратные уравнения Варианта 1.

1. x² + 5x - 6 = 0

   D = 5² - 4 × 1 × (-6) = 25 + 24 = 49

   x₁ = (-5 + √49) / (2 × 1) = (-5 + 7) / 2 = 2 / 2 = 1

   x₂ = (-5 - √49) / (2 × 1) = (-5 - 7) / 2 = -12 / 2 = -6

   Ответ: x₁ = 1, x₂ = -6

2. 3x² + 2x - 1 = 0

   D = 2² - 4 × 3 × (-1) = 4 + 12 = 16

   x₁ = (-2 + √16) / (2 × 3) = (-2 + 4) / 6 = 2 / 6 = 1 / 3

   x₂ = (-2 - √16) / (2 × 3) = (-2 - 4) / 6 = -6 / 6 = -1

   Ответ: x₁ = 1/3, x₂ = -1

3. x² - 8x - 84 = 0

   D = (-8)² - 4 × 1 × (-84) = 64 + 336 = 400

   x₁ = (8 + √400) / (2 × 1) = (8 + 20) / 2 = 28 / 2 = 14

   x₂ = (8 - √400) / (2 × 1) = (8 - 20) / 2 = -12 / 2 = -6

   Ответ: x₁ = 14, x₂ = -6

4. x² - 5x + 6 = 0

   D = (-5)² - 4 × 1 × 6 = 25 - 24 = 1

   x₁ = (5 + √1) / (2 × 1) = (5 + 1) / 2 = 6 / 2 = 3

   x₂ = (5 - √1) / (2 × 1) = (5 - 1) / 2 = 4 / 2 = 2

   Ответ: x₁ = 3, x₂ = 2

5. x² + 4x + 4 = 0

   D = 4² - 4 × 1 × 4 = 16 - 16 = 0

   x = -4 / (2 × 1) = -2

   Ответ: x = -2

6. 2x² + 3x + 1 = 0

   D = 3² - 4 × 2 × 1 = 9 - 8 = 1

   x₁ = (-3 + √1) / (2 × 2) = (-3 + 1) / 4 = -2 / 4 = -1 / 2

   x₂ = (-3 - √1) / (2 × 2) = (-3 - 1) / 4 = -4 / 4 = -1

   Ответ: x₁ = -1/2, x₂ = -1

7. 4x² + 10x - 6 = 0

   D = 10² - 4 × 4 × (-6) = 100 + 96 = 196

   x₁ = (-10 + √196) / (2 × 4) = (-10 + 14) / 8 = 4 / 8 = 1 / 2

   x₂ = (-10 - √196) / (2 × 4) = (-10 - 14) / 8 = -24 / 8 = -3

   Ответ: x₁ = 1/2, x₂ = -3

8. 3x² + 32x + 80 = 0

   D = 32² - 4 × 3 × 80 = 1024 - 960 = 64

   x₁ = (-32 + √64) / (2 × 3) = (-32 + 8) / 6 = -24 / 6 = -4

   x₂ = (-32 - √64) / (2 × 3) = (-32 - 8) / 6 = -40 / 6 = -20 / 3

   Ответ: x₁ = -4, x₂ = -20/3

9. x² - 2x - 48 = 0

   D = (-2)² - 4 × 1 × (-48) = 4 + 192 = 196

   x₁ = (2 + √196) / (2 × 1) = (2 + 14) / 2 = 16 / 2 = 8

   x₂ = (2 - √196) / (2 × 1) = (2 - 14) / 2 = -12 / 2 = -6

   Ответ: x₁ = 8, x₂ = -6

10. -x² = 5x - 14

    x² + 5x - 14 = 0

    D = 5² - 4 × 1 × (-14) = 25 + 56 = 81

    x₁ = (-5 + √81) / (2 × 1) = (-5 + 9) / 2 = 4 / 2 = 2

    x₂ = (-5 - √81) / (2 × 1) = (-5 - 9) / 2 = -14 / 2 = -7

    Ответ: x₁ = 2, x₂ = -7

11. x² + 7x + 2 = 0

    D = 7² - 4 × 1 × 2 = 49 - 8 = 41

    x₁ = (-7 + √41) / (2 × 1) = (-7 + √41) / 2

    x₂ = (-7 - √41) / (2 × 1) = (-7 - √41) / 2

    Ответ: x₁ = (-7 + √41) / 2, x₂ = (-7 - √41) / 2

12. 16x² - 9 = 0

    16x² = 9

    x² = 9 / 16

    x₁ = √(9 / 16) = 3 / 4

    x₂ = -√(9 / 16) = -3 / 4

    Ответ: x₁ = 3/4, x₂ = -3/4

13. -x² + x = 0

    x(-x + 1) = 0

    x₁ = 0

    -x + 1 = 0

    x = 1

    x₂ = 1

    Ответ: x₁ = 0, x₂ = 1

14. 3x² - 12x = 0

    3x(x - 4) = 0

    x₁ = 0

    x - 4 = 0

    x = 4

    x₂ = 4

    Ответ: x₁ = 0, x₂ = 4

15. x² + 2x = 0

    x(x + 2) = 0

    x₁ = 0

    x + 2 = 0

    x = -2

    x₂ = -2

    Ответ: x₁ = 0, x₂ = -2

16. -2x² + 14 = 0

    2x² = 14

    x² = 7

    x₁ = √7

    x₂ = -√7

    Ответ: x₁ = √7, x₂ = -√7

17. 6x² = 0

    x² = 0

    x = 0

    Ответ: x = 0

18. x² - 64 = 0

    x² = 64

    x₁ = √64 = 8

    x₂ = -√64 = -8

    Ответ: x₁ = 8, x₂ = -8

19. 6x(2x + 1) = 5x + 1

    12x² + 6x = 5x + 1

    12x² + x - 1 = 0

    D = 1² - 4 × 12 × (-1) = 1 + 48 = 49

    x₁ = (-1 + √49) / (2 × 12) = (-1 + 7) / 24 = 6 / 24 = 1 / 4

    x₂ = (-1 - √49) / (2 × 12) = (-1 - 7) / 24 = -8 / 24 = -1 / 3

    Ответ: x₁ = 1/4, x₂ = -1/3

20. (x - 2)² = 3x - 8

    x² - 4x + 4 = 3x - 8

    x² - 7x + 12 = 0

    D = (-7)² - 4 × 1 × 12 = 49 - 48 = 1

    x₁ = (7 + √1) / (2 × 1) = (7 + 1) / 2 = 8 / 2 = 4

    x₂ = (7 - √1) / (2 × 1) = (7 - 1) / 2 = 6 / 2 = 3

    Ответ: x₁ = 4, x₂ = 3