1. Rozwiąż równania; A) (2x-1)do kwadratu = 9 B) 1/2x do kwadratu-5x+8=0 2. Rozwiąż nierówność A) 3x do kwadratu -2x jest mniejsze 0 B)(x-2) do kwadratu jest większe (2x-1)(x-2)

zad 1 A) (2x - 1)² = 9 4x² - 4x + 1 - 9 = 0 4x² - 4x - 8 = 0 / : 4 x² - x - 2 = 0 Δ =(- 1)² - 4 * 1 * (- 2) = 1 + 8 = 9 √Δ = √9 = 3 x₁ = (1 - 3)/2 = - 2/2 = - 1 x₂ = (1 + 3)/2 = 4/2 = 2 B) 1/2x² - 5x + 8 = 0 / * 2 x² - 10x + 16 = 0 Δ = (- 10)² - 4 * 1 * 16 = 100 - 64 = 36 √Δ = √36 = 6 x₁ = (10 - 6)/2 = 4/2 = 2 x₂ = (10 + 6)/2 = 16/2 = 8 zad 2 A) 3x² - 2x < 0 Δ = (- 2)² - 4 * 3 * 0 = 4 √Δ = √4 = 2 x₁ = (2 - 2)/6 = 0/6 = 0 x₂ = (2 + 2)/6 = 4/6 = 2/3 a > 0 i Δ > 0 x ∈ (x₁ , x₂) x ∈ (0 , 2/3) B) (x - 2)² > (2x - 1)(x - 2) x² - 4x + 4 > 2x² - x - 4x + 2 x² - 4x + 4 - 2x² + x + 4x - 2 > 0 - x² + x + 2 > 0 Δ = 1² - 4 * (- 1) * 2 = 1 + 8 = 9 √Δ = √9 = 3 x₁ = (- 1 - 3)/(- 2) = - 4/- 2 = 2 x₂ = (- 1 + 3)/(- 2) = 2/- 2 = - 1 a < 0 i Δ > 0 x ∈ (x₂ , x₁) x ∈ (- 1 , 2)