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The positions of real numbers a and B on the number axis are shown in the figure ────┴──┴─────┴─────┴─┴──＞ b -1 0 a 1 A.a+b>0 B.ab>0 C.a-b>0 D.|a|>|b|
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RELATED INFORMATIONS
- 1. If two points a and B on the number axis represent real numbers a and B respectively, the length of line AB is () A. a-bB. a+bC. |a-b|D. |a+b|
- 2. An inequality is a formula that uses (), (), or () to represent the size relationship
- 3. Inequality is the expression of () relation
- 4. Inequalities are formulas that use symbols (), (), (), () to denote inequality relations The answers at the midpoint are greater than, less than, greater than or equal to, less than or equal to and not equal to But there are only the first four items in the book, which is not equal to the answer Please give me some advice But there is no sign "not equal" in the textbook, only greater than, less than, greater than or equal to, less than or equal to It is said in the textbook that, in general, formulas connected by the symbols "< (or" less than or equal to "), and" greater than "(or" ≥) are called inequalities. There is no ≠ sign
- 5. The expression of relation is called inequality
- 6. Under what circumstances does the direction of one variable linear inequality change When moving to? {x-4
- 7. Does the direction of the inequality sign change with the sign For example, | 2-x | > 3 2-x > 3, or 2-x < - 3 2-x > 3 x < 1 2-x < -3 x > -5 The meaning of the original formula | 2-x | > 3 on the number axis is that the distance from the far point is greater than 3 But in solving those two equations, the direction of the unequal sign changed So the solution set of the original formula should be {x | x < 1, or x > - 5} Or {x | - 5 < x < 1}
- 8. Why do negative numbers multiplied by both sides of inequality change sign
- 9. If both sides of the inequality divide or multiply by a number at the same time, the inequality does not change, right
- 10. Linear equations and inequalities of one variable 1. Let X / (a + B-C) = Y / (B + C-A) = Z / (a + C-B), find the value of (a-b) x + (B-C) y + (C-A) Z 2. Given / x + 5 / + / x-4 / = 9, find the value range of X (/ represents absolute value) 3. Cut two pieces of equal weight from two alloys of 7kg and 3kg respectively with different percentage of copper. Put the remaining part of each cut piece together with the rest of the other piece. After melting, the percentage of copper in the two alloys is equal. What is the weight of the cut alloy? 4. It is known that a, B and C are any real numbers, and it is proved that a ^ 2 + B ^ 2 + C ^ 2 > = AB + BC + ca 5. Given that x is a real number, prove 3 (1 + x ^ 2 + x ^ 4) > = (1 + X + x ^ 2) Only answer the third question, and don't answer the rest
- 11. The positions of real numbers a and B on the number axis are shown in the figure. Try to simplify | a + B | + | A-B | + | ab| -----b--------0--------a--------》
- 12. The position of the known real number AB on the number axis is shown in the figure: try to simplify: root (a-b) &# 178; - | a + B|
- 13. If point C is the golden section of line AB, and AC
- 14. If A-B = 1 + √ 3, B-C = 1 - √ 3, find the value of 1 / (A & # 178; + B & # 178; + C & # 178; - AB AC BC)
- 15. If a > b, C
- 16. Three inequalities are known: ① AB > 0. ② BC ad > 0. ③ C / a > D / b. taking two of them as conditions and the remaining one as conclusion, the number of correct propositions that can be formed is
- 17. In △ ABC, point D is the intersection of bisector of ∠ C and base ab. the following inequality is proved: CD & # 178; = AC · BC-AD · BD
- 18. What's the difference between the solution of inequality and the existence of inequality? For example, is x greater than 1-B / a the same as x greater than 1-B / a? Good and quick answer,
- 19. On the existence of inequalities For any real number x, the inequality │ x + 1 │ + X-2 │ > a holds, and the value range of real number a is obtained Analysis 2: using the absolute value inequality │ a │ - B │ ＜ a ± B │ ＜ a │ + B │ to solve the minimum value of F (x) = │ x + 1 │ + X-2 │ Let f (x) = x + 1 + X-2, x + 1 + X-2 = 3, f (x) min = 3. A < 3 Why can we do this?
- 20. Given C > 0, let P: function y = C ^ X be a decreasing function on R; Q: inequality x + | x-2c | >