Odpowiedź:
f(x) = x² + bx + 1
a = 1 , c = 1
x₁² + x₂² = 5
x₁² + x₂² = (x₁ + x₂)² - 2x₁x₂ = 5
Wzory Viet'a
x₁ + x₂ = - b/a = - b/1 = - b
x₁x₂ = c/a = 1/1 = 1
(x₁ + x₂)² - 2x₁x₂ = 5
(- b)² - 2 * 1 = 5
b² - 2 = 5
b² = 5 + 2 = 7
b² - 7 = 0
(b - √7)(b + √7) = 0
b - √7 = 0 ∨ b + √7 = 0
b = √7 ∨ b = - √7
