Verified answer

8а) x² + 8x + n = 0

По теореме Виета :

x₁ + x₂ = - 8

По условию :

x₁ - x₂ = 2 , значит 2 + x₂ + x₂ = - 8

2x₂ = - 10

x₂ = - 5

x₁ = - 8 - (- 5) = - 8 + 5 = - 3

n = x₁ * x₂ = - 3 * ( - 5) = 15

n = 15

8б) x² - 10x + n = 0

x₁ + x₂ = 10

x₁ - x₂ = 2

2 + x₂ + x₂ = 10

2x₂ = 8

x₂ = 4

x₁ = 2 + x₂ = 2 + 4 = 6

x₁ = 6

n = x₁ * x₂ = 6 * 4 = 24

n = 24

9a) 5x² - ax + 5 = 0

D = (-a)² - 4 * 5 * 5 = a² - 100

a² - 100 = 0

(a - 10)(a + 10) = 0

a - 10 = 0 a₁ = 10

a + 10 = 0 a₂ = - 10

5x² - 10x + 5 = 0

x₁ = 1

5x² + 10x + 5 = 0

x₂ = - 1

9б) 3x² - ax + 3 = 0

D =(-a)² - 4 * 3 * 3 = a² - 36

a² - 36 = 0

(a - 6)(a + 6) = 0

a - 6 = 0 a₁ = 6

a + 6 = 0 a₂ = - 6

3x² - 6x + 3 = 0

x₁ = 1

3x² + 6x + 3 = 0

x₂ = - 1