Решите неравенство:

а) (х + 9)⋅(х – 2)⋅(х – 15) < 0;

б) х(х – 5)⋅(х + 6) > 0;

в) (х – 1)⋅(х – 4)⋅(х – 8)⋅(х – 16) < 0.

Решение:

а) (х + 9) ⋅ (х – 2) ⋅ (х – 15) < 0;

(х + 9)⋅(х – 2)⋅(х – 15) = 0

x + 9 = 0 или x – 2 = 0 или x – 15 = 0

x = -9 x = 2 x = 15

x (-∞; – 9) U (2;15)

б) х(х – 5) ⋅ (х + 6) > 0;

х(х – 5)⋅(х + 6) = 0

x = 0 или x – 5 = 0 или x + 6 = 0

x = 5 x = – 6

x (-6; 0) U (5; + ∞)

в) (х – 1) ⋅ (х – 4) ⋅ (х – 8) ⋅ (х – 16) < 0.

(х – 1)⋅(х – 4)⋅(х – 8)⋅(х – 16) = 0

x -1 = 0; x – 4 = 0; x – 8 = 0; x – 16 = 0

x = 1 x = 4 x = 8 x = 16

x (1;4) U (8;16)

Источник : Учебник по Алгебре 9 класса авторов Ю.Н. Макарычев, Н.Г. Миндюк, К.И. Нешков, С.Б. Суворова, 2014г.