994. Решите уравнение: a) (x-7)²+3= (x - 2)(x + 2); б) (x+6)²-(x-5)(x + 5) = 79; в) (2x-3)²-(7-2x)² = 2; г) (5х1)² - (1-3x)² = 16x(x - 3).

a) (x-7)²+3= (x - 2)(x + 2)

x² - 14x + 49 + 3 = x² - 4

-14x = -4 - 49 - 3

-14x = -56

x = 4

б) (x+6)²-(x-5)(x + 5) = 79

x² + 12x + 36 - (x² - 25) = 79

x² + 12x + 36 - x² + 25 = 79

12x = 79 - 36 - 25

12x = 18

x = 18/12

x = 3/2 = 1.5

в) (2x-3)²-(7-2x)² = 2

4x² - 12x + 9 - (49 - 28x + 4x²) = 2

4x² - 12x + 9 - 49 + 28x - 4x² = 2

16x = 2 + 49 - 9

16x = 42

x = 42/16

x = 21/8 = 2.625

г) (5х-1)² - (1-3x)² = 16x(x - 3)

25x² - 10x + 1 - (1 - 6x + 9x²) = 16x² - 48x

25x² - 10x + 1 - 1 + 6x - 9x² = 16x² - 48x

16x² - 4x = 16x² - 48x

44x = 0

x = 0

Ответ: a) x = 4; б) x = 1.5; в) x = 2.625; г) x = 0