高级数学 | 高一下册 | 14.5 一元高次不等式 Higher Degree Inequalities in One Variable - 独中课程 | 线上补习

高中一 | 高级数学

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14.5 Higher Degree Inequalities in One Variable 一元高次不等式

Solve the inequalities
解下列不等式

(1) (2 – x)(x + 1)(x – 3) $\geq$ 0

(2) (2x – 3)(x – 1)(x + 1)(x + 3) < 0

(3)(a) (x – 3)(x – 1) $^2$ (x + 1) $^3$ (x + 3) $^4$ < 0

(3)(b) (x – 3)(x – 1) $^2$ (x + 1) $^3$ (x + 3) $^4$ > 0

(3)(c) (x – 3)(x – 1) $^2$ (x + 1) $^3$ (x + 3) $^4$ $\leq$ 0

(3)(d) (x – 3)(x – 1) $^2$ (x + 1) $^3$ (x + 3) $^4$ $\geq$ 0

(4) (x + 2)(x $^2$ – 2x – 4) > 0

(5) (1 – 2x)(x – 1)(x $^2$ + 2x + 3) < 0

(6) (x + 4)(x + 2) $^2$ > (3x – 2)(x + 2) $^2$

(1) x $\leq$ –1, 2 $\leq$ x $\leq$ 3

(2) –3 < x < –1, 1 < x < $\frac{3}{2}$

(3)(a) –1 < x < 1, 1 < x < 3

(3)(b) x < –3, –3 < x < –1, x > 3

(3)(c) –1 $\leq$ x $\leq$ 3, x = –3

(3)(d) x $\leq$ –1, x $\geq$ 3, x = 1

(4) -2 < x < 1 – $\sqrt5$ , x > 1 + $\sqrt5$

(5) x < $\frac{1}{2}$ , x > 1

(6) x < –2, –2 < x < 3