Classical examples of inequality scaling method,

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• 1. High school mathematics inequality proof Verification: 1 / 2-1 / (n + 1)
• 2. Scaling! The best problem of inequality scaling! If x, y, Z, a, B, C, R > 0, it is proved that: (x+y+a+b）/（x+y+a+b+c+r)+（y+z+b+c)/(y+z+a+b+c+r) >(x+z+a+c）/（x+z+a+b+c+r) The letters are right Don't worry about it
• 3. Contains the absolute value inequality formula foundation question, urgent! |f(x)|＜g(x) ==> -g(x)＜f(x)＜g(x) |F (x) | > G (x) = = > F (x) > G (x) or F (x) < - G (x) Is there any requirement for G (x) to make the above two formulas hold? The above two formulas hold when G (x) > 0 is mentioned in my reference book But when the teacher says and writes the topic, don't g (x) > 0, you can use the above formula If there is no requirement for G (x), can we write the derivation process of the above two formulas?
• 4. It is proved that: (a + b-2ab) (a + b-2) + (1-ab) ^ 2 = (A-1) ^ 2 (B-1) ^ 2
• 5. Let a > b > 0, the incorrect one in the following inequality is a.ab2ab / (a + b)
• 6. The needle of quadratic inequality of one variable There is a problem of quadratic inequality of one variable. I will use the method of drawing a thread. The problem is like this （x+2）（x+1）² ≥0 ——————— x-3 This problem is reduced to (x + 2) (x + 1) & sup2; (x-3) ≥ 0 I don't know what to do with a square
• 7. Given the function f (x) = LNX + (1-x) / ax, a is a constant greater than zero For any integer greater than one, lnn > 1 / 2 + 1 / 3 + 1/N
• 8. Mixed problems of inequality and function~ If the function f (x) = TX ^ 2 - (22T + 60) x + 144t (x > 0) (1) to make f (x) ≥ 0 hold, find the minimum value of T; (2) to make f (x) = 0, find the value range of X to make t > 20 hold
• 9. The problem of drawing number axis with the method of marked root >0 and 0 start up
• 10. How to solve higher order inequality?
• 11. Can expansion and contraction prove all inequalities?
• 12. Proof of inequality by the method of expansion and contraction The proof of loga (A-1) loga (a + 1) 2
• 13. A problem about solving inequality Xiaohua and her parents play on the seesaw. The total weight of the three people is 150kg. My father is sitting on one end of the seesaw. Xiaohua, who weighs only half of my mother, is sitting on the other end of the seesaw with my mother. At this time, my father's end is still on the ground. Please guess how many kilograms Xiaohua should weigh less than? Why?
• 14. Let X and y be positive real numbers, and 12 + X + 12 + y = 13, then the minimum value of XY is______ ．
• 15. It is urgent to solve this problem with inequality Xiaohua left home at 10:10 to catch the 11:00 train. It is known that his home is 10 kilometers away from the station. After he left home, he walked at a speed of 3 kilometers per hour for 5 minutes. Then he called the bus to the station and asked how many kilometers the bus should walk at least per hour so as not to miss the train?
• 16. A mathematics problem of grade two in junior high school, about inequality. Solving! Speed! It is known that integer x satisfies inequality (2x + 1) / 3 - 1 at the same time
• 17. Two difficult solutions to inequality 1. For any real number x, inequality-3 is known
• 18. The speed of solution set of inequality X-2 > 0 In this way, I forgot the previous knowledge
• 19. Find the solution of two inequalities 1) Let X and y be positive numbers and X + y = 1. Find the minimum value of 1 / x + 2 / Y and point out the value of X and y 2) When x is greater than 0, find the maximum value of 3x / x + 4
• 20. Master into, computing, solving equations, solving inequalities, to process, fast ah, speed The solution set of inequality system x + (2x-1) > 1 3x-1 > x + 2 is________ Calculation: (- 1 and 1 / 2 - 1 / 3 + 2 and 5 / 6) * - 12 Solution equation: (1-x) - X / 2 = x - (x-1 / 3 + 1) Solving the system of inequalities: 5 (x + 1) ＜ X-1, (5x-1) / 2 ＜ (11x + 1) / 4 + 3 If X-1 = 2, then x=_____