0 1 1. Add or discard some positive items (or negative items).
If you add some positive values to the polynomial, the value of the polynomial will become larger, and if you add some negative values to the polynomial, the value of the polynomial will become smaller. Because of the need to prove inequality, it is sometimes necessary to omit or add some terms to enlarge or narrow inequality, and to use the transitivity of inequality to achieve the purpose of proof.
02 2. Scale first and then sum (or sum first and then scale)
The left side of this inequality is not easy to sum. At this time, according to the characteristics of the right side of inequality, the numerator is changed into a constant first, and then the denominator is scaled, so that the sum can be made on the left side. If there are variables in the numerator and denominator at the same time, we should try to make one of them a constant, and the scaling of the fraction will take a positive score for the numerator and denominator. If amplification is needed, enlarge the numerator or reduce the denominator; If you need to reduce, you only need to reduce the numerator or enlarge the denominator.
03 3. Zoom first, then crack (or crack first, then zoom)
In this problem, we first reduce the denominator twice, then split the terms, and finally scale and aim at the target.
04 4. Zoom in or zoom out? Factor?
05 5. Zoom in or out item by item
06 6. Fix some projects and scale others.
This problem is enlarged and narrowed from the third item. When zooming in and out, you don't have to start with the first item, but you must treat it separately according to the specific questions, that is, you can't zoom in too wide or too narrow, just right.
07 7. Scaling with Basic Inequalities
08 8, first combine and sort appropriately, and then compare or scale item by item.
09 above introduction? Scaling method? Several commonly used strategies to prove inequality, the key to solving the problem lies in choosing the appropriate method according to the characteristics of the problem, and sometimes it is necessary to synthesize several methods. In the process of proof, proper scaling can simplify the complex, make the difficult easy, and achieve twice the result with half the effort. However, it is difficult to grasp the scope of scaling, and it often happens that no conclusion can be drawn or the opposite phenomenon can be drawn after scaling.
10 Therefore, how to determine the zoom target is particularly important when using the zoom method. In order to correctly determine the scale goal, we must grasp the characteristics of the topic according to the conclusion to be proved. Only by mastering the calibration skills, truly understanding and understanding, and adopting appropriate calibration methods according to different types of questions can we solve problems visually, thus cultivating and improving our thinking and logical reasoning abilities, as well as our ability to analyze and solve problems. I hope you can further understand the function of scaling methods and master the basic scaling methods and scaling adjustment means.