Контрольные задания > 1. x² - 3x + 2 = 0 2. x² - 4x + 3 = 0 3. x² - 5x + 4 = 0 4. x2 - 6x + 5 = 0 5. x² - 7x + 6 = 0 6. x² - 5x + 6 = 0 7. x² - 8x + 7 = 0 8. x² - 9x + 8 = 0 9. x2 - 6x + 8 = 0 10. x² - 11x + 10 = 0 11. x² - 7x + 10 = 0 12. x² - 13x + 12 = 0 13. x² - 8x +1 2 = 0 14. x² - 7x + 12 = 0 15. x² 525x + 4 = 0 16. x² - 3x + 2 = 0 17. x² - 11x + 24 = 0 18. x² - 10x + 24 = 0 19. x² - 13x + 36 = 0 20. x² - 16x + 48 = 0 21. x² - 17x + 52 = 0 22. x² - 27x + 72 = 0 23. x² - 17x + 60 = 0 24. x² - 13x + 42 = 0 25. x² - 11x + 28 = 0
Вопрос:

1. x² - 3x + 2 = 0 2. x² - 4x + 3 = 0 3. x² - 5x + 4 = 0 4. x2 - 6x + 5 = 0 5. x² - 7x + 6 = 0 6. x² - 5x + 6 = 0 7. x² - 8x + 7 = 0 8. x² - 9x + 8 = 0 9. x2 - 6x + 8 = 0 10. x² - 11x + 10 = 0 11. x² - 7x + 10 = 0 12. x² - 13x + 12 = 0 13. x² - 8x +1 2 = 0 14. x² - 7x + 12 = 0 15. x² 525x + 4 = 0 16. x² - 3x + 2 = 0 17. x² - 11x + 24 = 0 18. x² - 10x + 24 = 0 19. x² - 13x + 36 = 0 20. x² - 16x + 48 = 0 21. x² - 17x + 52 = 0 22. x² - 27x + 72 = 0 23. x² - 17x + 60 = 0 24. x² - 13x + 42 = 0 25. x² - 11x + 28 = 0

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Ответ:

Предмет: Математика

Класс: 8

Тип задания: Решение квадратных уравнений

Метод решения: Дискриминант

Давай решим уравнения по порядку, используя дискриминант.

  1. x² - 3x + 2 = 0

    D = (-3)² - 4 * 1 * 2 = 9 - 8 = 1

    x₁ = (3 + √1) / 2 = (3 + 1) / 2 = 2

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

  2. x² - 4x + 3 = 0

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

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

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

  3. x² - 5x + 4 = 0

    D = (-5)² - 4 * 1 * 4 = 25 - 16 = 9

    x₁ = (5 + √9) / 2 = (5 + 3) / 2 = 4

    x₂ = (5 - √9) / 2 = (5 - 3) / 2 = 1

  4. x² - 6x + 5 = 0

    D = (-6)² - 4 * 1 * 5 = 36 - 20 = 16

    x₁ = (6 + √16) / 2 = (6 + 4) / 2 = 5

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

  5. x² - 7x + 6 = 0

    D = (-7)² - 4 * 1 * 6 = 49 - 24 = 25

    x₁ = (7 + √25) / 2 = (7 + 5) / 2 = 6

    x₂ = (7 - √25) / 2 = (7 - 5) / 2 = 1

  6. x² - 5x + 6 = 0

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

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

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

  7. x² - 8x + 7 = 0

    D = (-8)² - 4 * 1 * 7 = 64 - 28 = 36

    x₁ = (8 + √36) / 2 = (8 + 6) / 2 = 7

    x₂ = (8 - √36) / 2 = (8 - 6) / 2 = 1

  8. x² - 9x + 8 = 0

    D = (-9)² - 4 * 1 * 8 = 81 - 32 = 49

    x₁ = (9 + √49) / 2 = (9 + 7) / 2 = 8

    x₂ = (9 - √49) / 2 = (9 - 7) / 2 = 1

  9. x² - 6x + 8 = 0

    D = (-6)² - 4 * 1 * 8 = 36 - 32 = 4

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

    x₂ = (6 - √4) / 2 = (6 - 2) / 2 = 2

  10. x² - 11x + 10 = 0

    D = (-11)² - 4 * 1 * 10 = 121 - 40 = 81

    x₁ = (11 + √81) / 2 = (11 + 9) / 2 = 10

    x₂ = (11 - √81) / 2 = (11 - 9) / 2 = 1

  11. x² - 7x + 10 = 0

    D = (-7)² - 4 * 1 * 10 = 49 - 40 = 9

    x₁ = (7 + √9) / 2 = (7 + 3) / 2 = 5

    x₂ = (7 - √9) / 2 = (7 - 3) / 2 = 2

  12. x² - 13x + 12 = 0

    D = (-13)² - 4 * 1 * 12 = 169 - 48 = 121

    x₁ = (13 + √121) / 2 = (13 + 11) / 2 = 12

    x₂ = (13 - √121) / 2 = (13 - 11) / 2 = 1

  13. x² - 8x + 12 = 0

    D = (-8)² - 4 * 1 * 12 = 64 - 48 = 16

    x₁ = (8 + √16) / 2 = (8 + 4) / 2 = 6

    x₂ = (8 - √16) / 2 = (8 - 4) / 2 = 2

  14. x² - 7x + 12 = 0

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

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

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

  15. x² - 25x + 4 = 0

    D = (-25)² - 4 * 1 * 4 = 625 - 16 = 609

    x₁ = (25 + √609) / 2

    x₂ = (25 - √609) / 2

  16. x² - 3x + 2 = 0

    D = (-3)² - 4 * 1 * 2 = 9 - 8 = 1

    x₁ = (3 + √1) / 2 = (3 + 1) / 2 = 2

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

  17. x² - 11x + 24 = 0

    D = (-11)² - 4 * 1 * 24 = 121 - 96 = 25

    x₁ = (11 + √25) / 2 = (11 + 5) / 2 = 8

    x₂ = (11 - √25) / 2 = (11 - 5) / 2 = 3

  18. x² - 10x + 24 = 0

    D = (-10)² - 4 * 1 * 24 = 100 - 96 = 4

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

    x₂ = (10 - √4) / 2 = (10 - 2) / 2 = 4

  19. x² - 13x + 36 = 0

    D = (-13)² - 4 * 1 * 36 = 169 - 144 = 25

    x₁ = (13 + √25) / 2 = (13 + 5) / 2 = 9

    x₂ = (13 - √25) / 2 = (13 - 5) / 2 = 4

  20. x² - 16x + 48 = 0

    D = (-16)² - 4 * 1 * 48 = 256 - 192 = 64

    x₁ = (16 + √64) / 2 = (16 + 8) / 2 = 12

    x₂ = (16 - √64) / 2 = (16 - 8) / 2 = 4

  21. x² - 17x + 52 = 0

    D = (-17)² - 4 * 1 * 52 = 289 - 208 = 81

    x₁ = (17 + √81) / 2 = (17 + 9) / 2 = 13

    x₂ = (17 - √81) / 2 = (17 - 9) / 2 = 4

  22. x² - 27x + 72 = 0

    D = (-27)² - 4 * 1 * 72 = 729 - 288 = 441

    x₁ = (27 + √441) / 2 = (27 + 21) / 2 = 24

    x₂ = (27 - √441) / 2 = (27 - 21) / 2 = 3

  23. x² - 17x + 60 = 0

    D = (-17)² - 4 * 1 * 60 = 289 - 240 = 49

    x₁ = (17 + √49) / 2 = (17 + 7) / 2 = 12

    x₂ = (17 - √49) / 2 = (17 - 7) / 2 = 5

  24. x² - 13x + 42 = 0

    D = (-13)² - 4 * 1 * 42 = 169 - 168 = 1

    x₁ = (13 + √1) / 2 = (13 + 1) / 2 = 7

    x₂ = (13 - √1) / 2 = (13 - 1) / 2 = 6

  25. x² - 11x + 28 = 0

    D = (-11)² - 4 * 1 * 28 = 121 - 112 = 9

    x₁ = (11 + √9) / 2 = (11 + 3) / 2 = 7

    x₂ = (11 - √9) / 2 = (11 - 3) / 2 = 4

Ответ: Решения приведены выше для каждого уравнения.

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