Rozwiąż równania i nierówności: a: 25x = 4x² b: 2(x-1)²-3<2x-2 c: -x³ - 2x² + x + 2 = 0 d: (x-3)(x²-16)=0

a) 25x = 4x² - 4x² + 25x = 0 - x(4x - 25) = 0   /·(-1) x(4x - 25) = 0 x = 0 ∧ 4x - 25 = 0 x = 0 lub 4x - 25 = 0 4x = 25    /:4 x = ²⁵/₄ x = 6¼ Odp. x  = 0 lub x = 6¼ b) 2(x - 1)² - 3 < 2x - 2 2(x² - 2x + 1) - 3 < 2x - 2 2x² - 4x + 2 - 3 - 2x + 2 < 0 2x² - 6x + 1 < 0 2x² - 6x + 1 = 0 Δ = 36 - 8 = 28; √Δ = √28 = √4·7 = 2√7 [latex]x_1 = frac{6 - 2sqrt{7}}{4} = frac{2(3 - sqrt{7})}{4} = frac{3 - sqrt{7}}{2}[/latex] [latex]x_2 = frac{6 + 2sqrt{7}}{4} = frac{2(3 + sqrt{7})}{4} = frac{3 + sqrt{7}}{2}[/latex] a = 2 > 0, czyli ramiona paraboli skierowane są w górę, zatem [latex]x in (frac{3-sqrt{7}}{2}; frac{3+sqrt{7}}{2})[/latex]   c) - x³ - 2x² + x + 2 = 0 - x²(x + 2) + 1(x + 2) = 0 (x + 2)(- x² + 1) = 0 (x + 2)(1² - x²) = 0 (x + 2)(1 - x)(1 + x) = 0 x + 2 = 0 ∨ 1 - x = 0 ∨ 1 + x = 0 x + 2 = 0 x = - 2 lub 1 - x = 0  - x = - 1  /·(- 1) x = 1 lub 1 + x = 0 x = - 1 Odp. x = - 2 lub x = 1 lub x = - 1   d) (x - 3)(x² - 16) = 0 (x - 3)(x² - 4²) = 0 (x - 3)(x - 4)(x + 4) = 0 x - 3 = 0 ∨ x - 4 = 0 ∨ x + 4 = 0 x - 3 = 0 x = 3 lub x - 4 = 0 x = 4 lub x + 4 = 0 x = - 4 Odp. x = 3 lub x = 4 lub x = - 4