Question

Решите квадратное уравнение :
4(4x−23)^2−19(4x−23)+12=0

Answer 1

Замена y = 4x - 23
             y² = (4x - 23)²

4y² - 19y + 12 = 0
D = b² - 4ac = 361 - 4 × 4 × 12 = 361 - 192 = 169 = 13²
y1 = (19 + 13) / 8 = 4
y2 = ( 19 - 13) / 8 = 0,75

Заменяем: при y1 = 4:
4x - 23 = 4
4 x = 23 + 4
4x = 27
x1 = 6,75

при y2 = 0,75:
4x - 23 = 0,75
4x = 23+ 0,75
4x = 23,75
x2 =5,9375