Решить уравнение 1)(3х+4)²+3(х-2)=46 2)2(1-1,5х)+2(х-2)²=1

Question

Решить уравнение
1)(3х+4)²+3(х-2)=46
2)2(1-1,5х)+2(х-2)²=1

Answer 1

1) (3x + 4)² + 3(x - 2) = 46
9x² +24x + 16 + 3x - 6 = 46
9x² + 27x -36 = 0
D = b² - 4·a·c = 27² - 4·9·(-36) = 729 +1296 = 2025, √D = 45
x = (- b +-√D)/(2·a)
x1 = (-27 + 45)/(2·9) = 18/18 = 1
x2 = (-27 - 45)/(2·9) = -72/18 = -4
Ответ: x1 = 1, x2 = 4

2) 2(1 - 1,5x) + 2(x - 2)² = 1
2 - 3x + 2(x² - 4x + 4) = 1
2 - 3x + 2x² - 8x + 8 = 1
2x² - 11x + 9 = 0
D = b² - 4·a·c  = (-11)²  - 4·2·9 = 49 √D = 7
x = (- b +-√D)/(2·a)
x1 = (11 + 7)/(2·2) = 18/4 = 4,5
x2 = (11 - 7)/(2·2) = 4/4 = 1
Ответ: x1 = 4,5, x2 = 1