Вариант 1 1) (x+7)(2-x) = 0 2) x² + 3x = 0 3) x² + 5x-6=0 4) 5x²+2x-3= 0 5) 2x-x²+3=0 6) 3x-1+4x2 = 0 7) x² + 8x = 9 8) x33 -4x2 = 9) 4x²-11x + 2 = 2x²+x-8 2 10) 4x²-19x + 32 = -6x²-6x + 41 2 11) (x − 9)² = -x² + 15x + 50 12) (x-3)(x + 3) = 5x - 13 13) 7(1-x) = (2x + 3)(1-x) 14) -x(4x + 1) = (x + 2)(x-2) 15) 5(x + 1)(x-3) = 4x² - 8x

Решаю данные уравнения.

1. (x+7)(2-x) = 0

   x+7 = 0 или 2-x = 0

   x = -7 или x = 2

   Ответ: x = -7, x = 2

2. x² + 3x = 0

   x(x+3) = 0

   x = 0 или x+3 = 0

   x = 0 или x = -3

   Ответ: x = 0, x = -3

3. x² + 5x - 6 = 0

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

   x = (-5 ± √49) / 2

   x₁ = (-5 + 7) / 2 = 1

   x₂ = (-5 - 7) / 2 = -6

   Ответ: x = 1, x = -6

4. 5x² + 2x - 3 = 0

   D = 2² - 4 * 5 * (-3) = 4 + 60 = 64

   x = (-2 ± √64) / (2 * 5)

   x₁ = (-2 + 8) / 10 = 6 / 10 = 0.6

   x₂ = (-2 - 8) / 10 = -10 / 10 = -1

   Ответ: x = 0.6, x = -1

5. 2x - x² + 3 = 0

   -x² + 2x + 3 = 0

   x² - 2x - 3 = 0

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

   x = (2 ± √16) / 2

   x₁ = (2 + 4) / 2 = 3

   x₂ = (2 - 4) / 2 = -1

   Ответ: x = 3, x = -1

6. 3x - 1 + 4x² = 0

   4x² + 3x - 1 = 0

   D = 3² - 4 * 4 * (-1) = 9 + 16 = 25

   x = (-3 ± √25) / (2 * 4)

   x₁ = (-3 + 5) / 8 = 2 / 8 = 0.25

   x₂ = (-3 - 5) / 8 = -8 / 8 = -1

   Ответ: x = 0.25, x = -1

7. x² + 8x = 9

   x² + 8x - 9 = 0

   D = 8² - 4 * 1 * (-9) = 64 + 36 = 100

   x = (-8 ± √100) / 2

   x₁ = (-8 + 10) / 2 = 1

   x₂ = (-8 - 10) / 2 = -9

   Ответ: x = 1, x = -9

8. x - 33 = -4x²

   4x² + x - 33 = 0

   D = 1² - 4 * 4 * (-33) = 1 + 528 = 529

   x = (-1 ± √529) / (2 * 4)

   x₁ = (-1 + 23) / 8 = 22 / 8 = 2.75

   x₂ = (-1 - 23) / 8 = -24 / 8 = -3

   Ответ: x = 2.75, x = -3

9. 4x² - 11x + 2 = 2x² + x - 8

   2x² - 12x + 10 = 0

   x² - 6x + 5 = 0

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

   x = (6 ± √16) / 2

   x₁ = (6 + 4) / 2 = 5

   x₂ = (6 - 4) / 2 = 1

   Ответ: x = 5, x = 1

10. 4x² - 19x + 32 = -6x² - 6x + 41

    10x² - 13x - 9 = 0

    D = (-13)² - 4 * 10 * (-9) = 169 + 360 = 529

    x = (13 ± √529) / (2 * 10)

    x₁ = (13 + 23) / 20 = 36 / 20 = 1.8

    x₂ = (13 - 23) / 20 = -10 / 20 = -0.5

    Ответ: x = 1.8, x = -0.5

11. (x - 9)² = -x² + 15x + 50

    x² - 18x + 81 = -x² + 15x + 50

    2x² - 33x + 31 = 0

    D = (-33)² - 4 * 2 * 31 = 1089 - 248 = 841

    x = (33 ± √841) / (2 * 2)

    x₁ = (33 + 29) / 4 = 62 / 4 = 15.5

    x₂ = (33 - 29) / 4 = 4 / 4 = 1

    Ответ: x = 15.5, x = 1

12. (x - 3)(x + 3) = 5x - 13

    x² - 9 = 5x - 13

    x² - 5x + 4 = 0

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

    x = (5 ± √9) / 2

    x₁ = (5 + 3) / 2 = 4

    x₂ = (5 - 3) / 2 = 1

    Ответ: x = 4, x = 1

13. 7(1 - x) = (2x + 3)(1 - x)

    7 - 7x = 2x - 2x² + 3 - 3x

    2x² - 6x + 4 = 0

    x² - 3x + 2 = 0

    D = (-3)² - 4 * 1 * 2 = 9 - 8 = 1

    x = (3 ± √1) / 2

    x₁ = (3 + 1) / 2 = 2

    x₂ = (3 - 1) / 2 = 1

    Ответ: x = 2, x = 1

14. -x(4x + 1) = (x + 2)(x - 2)

    -4x² - x = x² - 4

    5x² + x - 4 = 0

    D = 1² - 4 * 5 * (-4) = 1 + 80 = 81

    x = (-1 ± √81) / (2 * 5)

    x₁ = (-1 + 9) / 10 = 0.8

    x₂ = (-1 - 9) / 10 = -1

    Ответ: x = 0.8, x = -1

15. 5(x + 1)(x - 3) = 4x² - 8x

    5(x² - 2x - 3) = 4x² - 8x

    5x² - 10x - 15 = 4x² - 8x

    x² - 2x - 15 = 0

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

    x = (2 ± √64) / 2

    x₁ = (2 + 8) / 2 = 5

    x₂ = (2 - 8) / 2 = -3

    Ответ: x = 5, x = -3