Odpowiedź:
(2x + 6)/(x + 1) = x
założenie:
x + 1 ≠ 0
x ≠ - 1
D: x ∈ R \ { - 1 }
(2x + 6)/(x + 1) = x | * (x + 1)
2x + 6 = x(x + 1)
2x + 6 = x² + x
x² + x - 2x - 6 = 0
x² - x + 6 = 0
a = 1 , b = - 1 , c = - 6
Δ = b² - 4ac = (- 1)² - 4 * 1 * (- 6) = 1 + 24 = 25
√Δ = √25 = 5
x₁ = (- b - √Δ)/2a = (1 - 5)/2 = - 4/2 = - 2
x₂ = (- b + √Δ)/2a = (1 + 4)/2 = 5/2 = 2,5
