1) [x2 + 2(x – 1) - x(1 + x)][(x – 2)2 + 6x] > (x – 2)[x(x + 2) + 4] [non esiste x appart. ad R]2) (x – 4)(x + 6)(x + 5) ≥ 0 [-6 ≤ x ≤ -5 U x ≥ 4]3) 4(x2 - 1) + (x + 1)(x – 3) < 0 [-1 < x < 7/5]4) 2x(x + 1) – (x2 + 1) < 2x2 [x ≠ 1]5) x3(1 + x) < 2x2(x2 – 2x - 3) [x < -1 U x > 6]6) [(3x – 2) / x] - 4 ≤ 0 [x ≤ -2 U x > 0]7) [5 / (x – 3)] + [x / (x + 2)] + [5x / (x + 2)(x – 3)] > 0 [x < -5 U x > 3][a cura di Walter Caputo – 4-11-2008]
ESERCIZIO 17 PER STUDENTI 3^ IGEA: Disequazioni assortite
1) [x2 + 2(x – 1) - x(1 + x)][(x – 2)2 + 6x] > (x – 2)[x(x + 2) + 4] [non esiste x appart. ad R]2) (x – 4)(x + 6)(x + 5) ≥ 0 [-6 ≤ x ≤ -5 U x ≥ 4]3) 4(x2 - 1) + (x + 1)(x – 3) < 0 [-1 < x < 7/5]4) 2x(x + 1) – (x2 + 1) < 2x2 [x ≠ 1]5) x3(1 + x) < 2x2(x2 – 2x - 3) [x < -1 U x > 6]6) [(3x – 2) / x] - 4 ≤ 0 [x ≤ -2 U x > 0]7) [5 / (x – 3)] + [x / (x + 2)] + [5x / (x + 2)(x – 3)] > 0 [x < -5 U x > 3][a cura di Walter Caputo – 4-11-2008]