Решение
x² + 2px + 1 = 0
D = 4p² - 4*1*1 = 4(p² - 1)
x₁ = (- 2p - 2√(p² - 1)) /2
x₁ = - p - √(p² - 1)
x₂ = (- 2p + 2√(p² - 1)) /2
x₂ = - p + √(p² - 1)
x₁ : x₂ = 9
[- p - √(p² - 1)] : [- p + √(p² - 1)] = 9
- p - √(p² - 1) = 9 * [- p + √(p² - 1)]
- p - √(p² - 1) = - 9p + 9√(p² - 1)
- 9p + 9√(p² - 1) + p + √(p² - 1) = 0
10√(p² - 1) = 8p
[10√(p² - 1)]² = (8p)²
100(p² - 1) = 64p²
100p² - 100 - 64p² = 0
36p² = 100
p² = 100/36
p₁ = - 10/6 = - 5/3 = - 1 (2/3)
p₂ = 10/6 = 1 (2/3)