In fact, in essence, for an inequality problem, you can use any given inequality at will, and it doesn't matter if you use it many times in a row, as long as you ensure that the direction of the inequality is always right. However, the maximum problem is more demanding than the inequality problem, and the equal sign is required. Therefore, when solving the maximum problem with inequality, there are two steps (taking the minimum value of x as an example): 1. Scaling with inequality, X≥a is obtained (note that a is a known value, not a function, which means "one side is a fixed value", but personally it is easy to cause misunderstanding). 2. Explain that X=a can be established (the common situation here is that X≥a is composed of several inequalities, such as X ≥ Y ≥ Z ≥ A. At this time, in order to explain that X=a can be established, it is only necessary to explain that each inequality above can be established "="). As long as these two points are achieved, the method must be correct. Let's use this standard to look at your example.

Look at this example in your question first. First, scaling to get t≥2+ root number 2 is definitely no problem. Secondly, you zoom in and out in two steps. The first equals sign is a=b, and the second equals sign is t=2+ root sign 2. When a=b= 1+ root 2/2, both inequalities are equal signs. So there is no problem with this practice.

Look at the question you asked on the second floor. The mistake is that I said 1. Not satisfied. This proof does not convert x 2+4/x into a fixed value ≥ a.x 2+4/x ≥ 4 √ X. This formula is correct, but the right side is not a fixed value, so a lower bound cannot be obtained by this formula (the concept of "lower bound" as the name implies). The following reasoning is also unreasonable, just like through a >；; B, C = D, and then a >；; Ding is just as ridiculous. The key is that 4√x is not a fixed value. When x is different, 4√x can be either top B or top D. Using it as a medium, the sizes of A and C cannot be deduced.

In short, the saying that "one party is a fixed value" has some truth, but it is easy to cause misunderstanding. In fact, the scaling process may be composed of multiple inequalities, and each inequality does not necessarily have a fixed value (for example, in the step of t≥2√(t+ 1) in your question, both sides are not fixed values), but it is necessary to finally get a fixed value as the lower bound. I suggest that the landlord use what I said above 1 2 to understand, including the contents in brackets there.

P.S. "Dante Fiction" netizens said that the proposition of triangle congruence judgment is correct. In the case of edges and angles, if that angle is obtuse, we can really judge congruence. I think the above answer is related to dantafiction and reliable. However, I think what he said is somewhat absolute. There is some truth in the sentence "One side is a fixed value". The key is to understand the essence of this sentence, not just the literal meaning. Many mistakes or dogmas are caused by understanding certain formulas word for word. If the landlord understands the two things I said above, this formula will do ~ ~ I hope my answer will be helpful to the landlord:)