РЕШЕНИЕ:

1/x²+ 2/x−3=0

1+ 2x−3x²=0

3x² - 2x - 1 =0

D = 2² - 4∙3∙(-1) = 4 + 12 = 16 = 4²

x¹ = (2 + 4) / 6 = 6 / 6 = 1

x² = (2 - 4) / 6 = - 2 / 6 = - 1/3

Ответ: 1; - 1/3

РЕШЕНИЕ:

1/(x−1)² + 2/(x−1) − 3 = 0

1 + 2(х - 1) - 3(х-1)² = 0

1 + 2х - 2 - 3(х² - 2х + 1) = 0

2х - 1 - 3х² + 6х - 3 = 0

- 3х² + 8х - 4 = 0

3х² - 8х + 4 = 0

D = (-8)² - 4∙3∙4 = 64 - 48 = 16 = 4²

x₁ = ( 8 - 4) / 6 = 4 / 6 = 2/3

x₂ = ( 8 + 4) / 6 = 12 / 6 = 2

Ответ: 2/3 ; 2

РЕШЕНИЕ:

1/x²−1/x−6=0

1−1x−6x²=0

6x² + 1x - 1 =0

D = 1² - 4∙6∙(-1) = 1 + 24 = 25 = 5²

x¹ = (-1 + 5) / 12 = 4 / 12 = 1/3

x² = (-1 - 5) / 12 = - 6/ 12 = - 1/2

Ответ: 1/3 ; - 1/2

РЕШЕНИЕ:

1/(x−2)² - 1/(x−2) − 6 = 0

1 - 1(х - 2) - 6(х-2)² = 0

1 - х + 2 - 6 (х² - 4х + 4) = 0

- х + 3 - 6х² + 24х - 24 = 0

- 6х² + 23х - 21 = 0

6х² - 23х + 21 = 0

D = (-23)² - 4∙6∙21 = 529 - 504 = 25 = 5²

x₁ = (23 - 5) / 12 = 18 / 12 = 1.5

x₂ = (23 + 5) / 12 = 28 / 12 = 7/3

Ответ: 1.5 ; 7/3

РЕШЕНИЕ:

1/x²+3/x−10=0

1+3x−10x²=0

10x² - 3x - 1 =0

D = 3² - 4∙10∙(-1) = 9 + 40 = 49 = 7²

x¹ = (3 + 7) / 20 = 10 / 20 = 1/2

x² = (3 - 7) / 20 = - 4 / 20 = - 1/5

Ответ: 1/2 ; - 1/5

РЕШЕНИЕ:

1/(x−1)² + 3/(x−1) − 10 = 0

1 + 3(х - 1) - 10(х-1)² = 0

1 + 3х - 3 - 10 (х² - 2х + 1) = 0

3х - 2 - 10х² + 20х - 10 = 0

- 10х² + 23х - 12 = 0

10х² - 23х + 12 = 0

D = (-23)² - 4∙10∙12 = 529 - 480 = 49 = 7²

x₁ = (23 - 7) / 20 = 16 / 20 = 0.8

x₂ = (23 + 7) / 20 = 30 / 20 = 1.5

Ответ: 0.8 ; 1.5