Задание 4. Найдите корень уравнения. 1) (x-4)2-x2=0 2) (x-6)2-x2= 0 3) (x-5)²-x2=0 4) (x-7)2-x2=0 5) (2x-1)²-4x2 =0 6) (2x-5)²-4x2 = 0 7) (3x-6)²-9x2=0 8) (2x-6)2-4x2 = 0 9) (x-5)²=(x-7)² 10) (x-8)2=(x+2)² 11) (x+3)2=(x+5)2 12) (x+11)2=(x-9)2

Задание 4

1. (x - 4)² - x² = 0

   x² - 8x + 16 - x² = 0

   -8x + 16 = 0

   -8x = -16

   x = 2

   Ответ: x = 2

2. (x - 6)² - x² = 0

   x² - 12x + 36 - x² = 0

   -12x = -36

   x = 3

   Ответ: x = 3

3. (x - 5)² - x² = 0

   x² - 10x + 25 - x² = 0

   -10x = -25

   x = 2.5

   Ответ: x = 2.5

4. (x - 7)² - x² = 0

   x² - 14x + 49 - x² = 0

   -14x = -49

   x = 3.5

   Ответ: x = 3.5

5. (2x - 1)² - 4x² = 0

   4x² - 4x + 1 - 4x² = 0

   -4x = -1

   x = 0.25

   Ответ: x = 0.25

6. (2x - 5)² - 4x² = 0

   4x² - 20x + 25 - 4x² = 0

   -20x = -25

   x = 1.25

   Ответ: x = 1.25

7. (3x - 6)² - 9x² = 0

   9x² - 36x + 36 - 9x² = 0

   -36x = -36

   x = 1

   Ответ: x = 1

8. (2x - 6)² - 4x² = 0

   4x² - 24x + 36 - 4x² = 0

   -24x = -36

   x = 1.5

   Ответ: x = 1.5

9. (x - 5)² = (x - 7)²

   x² - 10x + 25 = x² - 14x + 49

   4x = 24

   x = 6

   Ответ: x = 6

10. (x - 8)² = (x + 2)²

    x² - 16x + 64 = x² + 4x + 4

    -20x = -60

    x = 3

    Ответ: x = 3

11. (x + 3)² = (x + 5)²

    x² + 6x + 9 = x² + 10x + 25

    -4x = 16

    x = -4

    Ответ: x = -4

12. (x + 11)² = (x - 9)²

    x² + 22x + 121 = x² - 18x + 81

    40x = -40

    x = -1

    Ответ: x = -1