Решение:
1) (7x+1)(3x-1) - 21^2 = 321x^2 - 7x + 3x - 1 - 441 = 321x^2 - 4x - 442 = 0Теперь найдем корни этого квадратного уравнения:D = (-4)^2 - 421(-442) = 16 + 36936 = 36952
x1 = (-(-4) + sqrt(36952)) / 42x1 = (4 + 192) / 42x1 = 196 / 42x1 = 14/3
x2 = (-(-4) - sqrt(36952)) / 42x2 = (4 - 192) / 42x2 = -188 / 42x2 = -94/21
Ответ: x1 = 14/3, x2 = -94/21
2) (1-4x)(1-3x) = 6x(2x-1)1 - 3x - 4x + 12x^2 = 12x^2 - 6x12x^2 - 7x - 1 = 0D = (-7)^2 - 412(-1) = 49 + 48 = 97
x1 = (7 + sqrt(97)) / 24x1 = (7 + sqrt(97)) / 24
x2 = (7 - sqrt(97)) / 24x2 = (7 - sqrt(97)) / 24
Ответ: x1 = (7 + sqrt(97)) / 24, x2 = (7 - sqrt(97)) / 24
Решение:
1) (7x+1)(3x-1) - 21^2 = 3
21x^2 - 7x + 3x - 1 - 441 = 3
21x^2 - 4x - 442 = 0
Теперь найдем корни этого квадратного уравнения:
D = (-4)^2 - 421(-442) = 16 + 36936 = 36952
x1 = (-(-4) + sqrt(36952)) / 42
x1 = (4 + 192) / 42
x1 = 196 / 42
x1 = 14/3
x2 = (-(-4) - sqrt(36952)) / 42
x2 = (4 - 192) / 42
x2 = -188 / 42
x2 = -94/21
Ответ: x1 = 14/3, x2 = -94/21
2) (1-4x)(1-3x) = 6x(2x-1)
1 - 3x - 4x + 12x^2 = 12x^2 - 6x
12x^2 - 7x - 1 = 0
D = (-7)^2 - 412(-1) = 49 + 48 = 97
x1 = (7 + sqrt(97)) / 24
x1 = (7 + sqrt(97)) / 24
x2 = (7 - sqrt(97)) / 24
x2 = (7 - sqrt(97)) / 24
Ответ: x1 = (7 + sqrt(97)) / 24, x2 = (7 - sqrt(97)) / 24