1. Решите уравнения a) (x + 4)2 - x(x + 5) = 5 6) x² - (x - 7)2 = -28 B) (x+4)(x-4) = 2x(x + 3) - x2 г) (2x + 1)² - (5 - 2x)2 = 0 д) (6x - 5)2 + 1 = (4x + 2)(9x-4) e) (7-16x)(2+9x) + (1-12x)2 = 0 ж) (8 – 15)(8x + 15) - (5x)² = 39x2 + x 3) 5x2 - (3x - 2)(3x + 4) = 8x - 4x2 и) (х - 9)2 = (5-x)2 2. Найдите значение выражений a) (y+3)2 +y(1 - y); y = 2 6) (m+9)(m – 9) – m(m + 8); m = 4 в) (За - 1)2 - 9a(5 + a); a = 3,7 r) 8x(2x + 8) - (4x - 7)2; x = д) (10x - 1)² - (25x-3) (-1+ 4x); x = -5 e) (2x-5)(2x + 5) - (2x)2; x = 4,7 ж) 7x(x+9)+(5x+8)(8-5)-32x2; x = - 3) у² - 4x + 4 - (y + 3)2; y = 5,8 и) (x + 8)² + x(4 - x); x = -3

1. Решите уравнения

1. a) (x + 4)² - x(x + 5) = 5

   Разберем уравнение:

   (x² + 8x + 16) - (x² + 5x) = 5

   x² + 8x + 16 - x² - 5x = 5

   3x + 16 = 5

   3x = -11

   x = -11/3

2. б) x² - (x - 7)² = -28

   x² - (x² - 14x + 49) = -28

   x² - x² + 14x - 49 = -28

   14x = 21

   x = 3/2

3. в) (x + 4)(x - 4) = 2x(x + 3) - x²

   (x² - 16) = 2x² + 6x - x²

   x² - 16 = x² + 6x

   6x = -16

   x = -8/3

4. г) (2x + 1)² - (5 - 2x)² = 0

   (4x² + 4x + 1) - (25 - 20x + 4x²) = 0

   4x² + 4x + 1 - 25 + 20x - 4x² = 0

   24x - 24 = 0

   24x = 24

   x = 1

5. д) (6x - 5)² + 1 = (4x + 2)(9x - 4)

   36x² - 60x + 25 + 1 = 36x² + 18x - 16x - 8

   36x² - 60x + 26 = 36x² + 2x - 8

   -62x = -34

   x = 17/31

6. e) (7 - 16x)(2 + 9x) + (1 - 12x)² = 0

   14 + 63x - 32x - 144x² + 1 - 24x + 144x² = 0

   7x + 15 = 0

   7x = -15

   x = -15/7

7. ж) (8x – 15)(8x + 15) - (5x)² = 39x² + x

   64x² - 225 - 25x² = 39x² + x

   39x² - 225 = 39x² + x

   x = -225

   x = -225

8. з) 5x² - (3x - 2)(3x + 4) = 8x - 4x²

   5x² - (9x² + 12x - 6x - 8) = 8x - 4x²

   5x² - 9x² - 6x + 8 = 8x - 4x²

   -4x² - 6x + 8 = 8x - 4x²

   -14x = -8

   x = 4/7

9. и) (x - 9)² = (5 - x)²

   x² - 18x + 81 = 25 - 10x + x²

   -8x = -56

   x = 7

2. Найдите значение выражений

1. a) (y + 3)² + y(1 - y); y = 2

   (2 + 3)² + 2(1 - 2) = 25 + 2(-1) = 25 - 2 = 23

   Результат: 23

2. б) (m + 9)(m – 9) – m(m + 8); m = 4

   (4 + 9)(4 - 9) - 4(4 + 8) = 13(-5) - 4(12) = -65 - 48 = -113

   Результат: -113

3. в) (3a - 1)² - 9a(5 + a); a = 3,7

   (3 * 3.7 - 1)² - 9 * 3.7(5 + 3.7) = (11.1 - 1)² - 33.3(8.7) = 10.1² - 289.71 = 102.01 - 289.71 = -187.7

   Результат: -187.7

4. г) 8x(2x + 8) - (4x - 7)²; x = 3/8

   8 * (3/8)(2 * (3/8) + 8) - (4 * (3/8) - 7)² = 3(3/4 + 8) - (3/2 - 7)² = 3(35/4) - (-11/2)² = 105/4 - 121/4 = -16/4 = -4

   Результат: -4

5. д) (10x - 1)² - (25x - 3)(-1 + 4x); x = -5

   (10(-5) - 1)² - (25(-5) - 3)(-1 + 4(-5)) = (-50 - 1)² - (-125 - 3)(-1 - 20) = (-51)² - (-128)(-21) = 2601 - 2688 = -87

   Результат: -87

6. e) (2x - 5)(2x + 5) - (2x)²; x = 4,7

   (2 * 4.7 - 5)(2 * 4.7 + 5) - (2 * 4.7)² = (9.4 - 5)(9.4 + 5) - (9.4)² = (4.4)(14.4) - 88.36 = 63.36 - 88.36 = -25

   Результат: -25

7. ж) 7x(x + 9) + (5x + 8)(8 - 5x) - 32x²; x = -5/6

   7 * (-5/6)(-5/6 + 9) + (5 * (-5/6) + 8)(8 - 5 * (-5/6)) - 32 * (-5/6)² = (-35/6)(49/6) + (-25/6 + 48/6)(48/6 + 25/6) - 32 * (25/36) = (-35/6)(49/6) + (23/6)(73/6) - 32 * (25/36) = -1715/36 + 1679/36 - 800/36 = -836/36 = -209/9

   Результат: -209/9

8. з) y² - 4x + 4 - (y + 3)²; y = 5,8

   (5.8)² - 4x + 4 - (5.8 + 3)² = 33.64 - 4x + 4 - (8.8)² = 37.64 - 4x - 77.44 = -39.8 - 4x

   Нужно значение x, чтобы вычислить до конца.

9. и) (x + 8)² + x(4 - x); x = -3

   (-3 + 8)² + (-3)(4 - (-3)) = (5)² + (-3)(7) = 25 - 21 = 4

   Результат: 4