РЕШЕНИЕ:

1/x²−3/x−4=0

1−3x−4x²=0

4x² + 3x - 1 =0

D = 3² - 4∙4∙(-1) = 9 + 16 = 25 = 5²

x¹ = (-3 + 5) / 8 = 2 / 8 = 0.25

x² = (-3 - 5) / 8 = - 8 / 8 = - 1

Ответ: 0.25; - 1

РЕШЕНИЕ:

1/(x−3)² - 3/(x−3) − 4 = 0

1 - 3(х - 3) - 4(х-3)² = 0

1 - 3х + 9 - 4 (х² - 6х + 9) = 0

-3х + 10 - 4х² + 24х - 36 = 0

- 4х² + 21х - 26 = 0

4х² - 21х + 26 = 0

D = (-21)² - 4∙4∙26 = 441 - 416 = 25 = 5²

x₁ = (21 - 5) / 8 = 16 / 8 = 2

x₂ = (21 + 5) / 8 = 26 / 8 = 13/4 = 3.25

Ответ: 2; 3.25

РЕШЕНИЕ:

1/x²+ 4/x−12=0

1 + 4x−12x²=0

12x² - 4x - 1 =0

D = 4² - 4∙12∙(-1) = 16 + 48 = 64 = 8²

x¹ = (4 - 8) / 24 = - 4 / 24 = - 1/6

x² = (4 + 8) / 24 = 12 / 24 = 1/2 = 0.5

Ответ: - 1/6 ; 0.5

РЕШЕНИЕ:

1/(x−1)² + 4/(x−1) − 12 = 0

1 + 4(х - 1) - 12(х-1)² = 0

1 + 4х - 4 - 12 (х² - 2х + 1) = 0

4х - 3 - 12х² + 24х - 12 = 0

- 12х² + 28х - 15 = 0

12х² - 28х + 15 = 0

D = (-28)² - 4∙12∙15 = 784 - 720 = 64 = 8²

x₁ = (28 - 8) / 24 = 20 / 24 = 5/6

x₂ = (28 + 8) / 24 = 36 / 24 = 3/2

Ответ: 5/6 ; 3/2