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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

14.7 无理不等式 Irrational Inequalities
14.7 Irrational Inequalities 无理不等式


Solve the inequalities
解下列不等式

(1)  \sqrt{3x+2}-3 < 0
Answer:
-\frac{2}{3} \leq x < \frac{7}{3}
(2)  1-\sqrt{3-x} < 0
Answer:
x < 2
(3)  2+\sqrt{1-3x}\le0
Answer:
无解
(4)  \sqrt{2x+3}+2>0
Answer:
x \geq -\frac{3}{2}
(5)  \sqrt{x^2+2x}-\sqrt{4-x}>0
Answer:
x < -4 , 1< x \leq 4
(6)  \sqrt{9-x}-\sqrt{2x-1}\geq0
Answer:
\frac{1}{2} \leq x \leq 3\frac{1}{3}
(7)  \sqrt{2-x}<x+4
Answer:
-2 < x \leq 2
(8)  \sqrt{x+1}\le x-1
Answer:
x \geq 3
(9)  \sqrt{5-x}>x-3
Answer:
x < 4
(10)  \sqrt{x^2-4}>x-1
Answer:
x \leq -2 , x > 2\frac{1}{2}
(11)  \sqrt{x+1}-\sqrt x>\sqrt{x-1}
Answer:
1 \leq x < \frac{2}{\sqrt3}
(12)  \sqrt{x+5}-\sqrt x-\sqrt{x-3}>0
Answer:
3 < x < 4