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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

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

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

Answer :

(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