Odpowiedź:
a₁ = 2
a₂ = x - 1
a₃ = x + 1
a₃/a₂ = a₂/a₁
(x + 1)/(x - 1) = (x - 1)/2
założenie :
x - 1 ≠ 0
x ≠ 1
D: x ∈ R \ {1}
2(x + 1) = (x - 1)(x - 1)
2x + 2 = (x - 1)²
2x + 2 = x² - 2x + 1
x² - 2x - 2x + 1 - 2 = 0
x² - 4x - 1 = 0
a = 1 , b = - 4 , c = - 1
Δ = b² - 4ac(- 4)² - 4 * 1 * (- 1) = 16 + 4 = 20
√Δ = √20 = √(4 * 5) = 2√5
x₁ = ( - b - √Δ)/2a = (4 - 2√5)/2 = 2(2 - √5)/2 = 2 - √5
x₂ = (- b + √Δ)/2a = (4 + 2√5)/2a = 2(2 + √5)/2 = 2 + √5
a = 2 , b = 2 - √5 - 1 = 1 - √5 , c = 2 - √5 + 1 = 3 - √5
lub
a = 2 , b = 2 + √5 - 1 = 1 + √5 , c = 2 + √5 + 1 = 3 + √5
