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