a) W(x) = (2x² + 3)(x – 1) – (x – 1)(x² + 5)
W(x) = (x – 1)[2x² + 3 – (x² + 5)]
W(x) = (x – 1)(2x² + 3 – x² – 5)
W(x) = (x – 1)(x² – 2)
W(x) = (x – 1)(x – √2)(x + √2)
(x – 1)(x – √2)(x + √2) > 0
x – 1 = 0, x – √2 = 0, x + √2 = 0
x = 1, x = √2, x = –√2
*szkic wykresu w załączniku*
x ∈ (–√2, 1) ∪ (√2, ∞)
b) W(x) = 12x³ + 20x² – 27x – 45
W(x) = 4x²(3x + 5) – 9(3x + 5)
W(x) = (4x² – 9)(3x + 5)
W(x) = (2x – 3)(2x + 3)(3x + 5)
(2x – 3)(2x + 3)(3x + 5) ≤ 0
2x – 3 = 0, 2x + 3 = 0, 3x + 5 = 0
2x = 3, 2x = –3, 3x = –5
x = 1½, x = –1½, x = –1⅔
*szkic wykresu w załączniku*
x ∈ (–∞, –1⅔⟩ ∪ ⟨–1½, 1½⟩
c) W(x) = (9x² – 6x + 1) – (4x² + 20x + 25)
W(x) = (3x – 1)² – (2x + 5)²
W(x) = (3x – 1 + 2x + 5)[3x – 1 – (2x + 5)]
W(x) = (5x + 4)(x – 6)
(5x + 4)(x – 6) < 0
5x + 4 = 0, x – 6 = 0
5x = –4, x = 6
x = –⅘, x = 6
*szkic wykresu w załączniku*
x ∈ (–⅘, 6)
