Chapter 8 Leading the Bad Guys
Gong Rihui's brows twitched fiercely. He felt that this guy was pretending, but he couldn't say anything. After all, this reason was normal.
"This problem-solving method can broaden your thinking and will be of great help to you in the future. But at this stage, I still recommend using conventional methods to solve problems. You should retain this kind of problem-solving thinking, but you cannot do it because of Walking alone and forgetting the original method. ”
"After all, sometimes the more basic something is, the more truth it contains."
"Also, what have you learned about mathematics in college?"
Gong Rihui looked at Xu Chuan and asked, "This kid's talent is really one of the best he has ever seen in his teaching life. It would be a waste not to learn mathematics."
Maybe this competition is an opportunity. If you teach him well, you might be able to turn him into mathematics. After all, he is only seventeen years old, so it is not too late to start learning now.
"I've almost finished reading advanced algebra, differential geometry, partial differential equations, and ordinary differential equations."
Xu Chuan selected some college mathematics answers that are needed to study physics.
Although he must have learned more mathematics than these, those deeper things and mathematics that are not used in competition with objects are obviously not suitable to be mentioned now.
"Oh? Then I'll give you another question."
Gong Rihui was a little surprised. He didn't expect that this kid had seen so much college mathematics, which was comparable to students who could enter the national team.
He casually took out a piece of scratch paper and pen from Xu Chuan's desk, and sat down on the desk next to him.
A quarter of an hour later, a piece of paper with two questions returned to Xu Chuan's desk.
"Give me the answer tomorrow."
After saying that, Gong Rihui returned to the podium and continued to drink tea, read newspapers and fish.
"Show me, show me, Brother Chuan."
Next to him, the round-faced Lu Tianrui came over curiously. Although he had not finished the two questions on the blackboard, it did not affect his enjoyment at all.
Lu Tianrui grabbed the manuscript paper from the table and looked over it impatiently. However, the next second, he began to doubt his life.
1. Find the smallest real number M such that the inequality is true for all real numbers a, b, c
|ab(a-b)+bc(b-c)+ca(c-a)|≤M(a+b+c)
2. .
The first question caught his eye, but before he even read the second question, Lu Tianrui was a little dumbfounded. He couldn't find a place to start with an inequality at the first time.
How to find the smallest real number M?
First change the formula to make both sides equal? Or precondition? It seems like nothing works?
After studying for a while, he still couldn't figure out how to solve the problem. He lay down on the chair, stared at the ceiling silently, and began to doubt life.
"Is it so difficult?"
Xu Chuan took the manuscript paper over curiously, but it was snatched away before he could even read the question. Would this force a mathematical genius to become autistic?
"One to find inequalities and one to find matrices. It looks interesting."
Xu Chuan stared at the two questions. The knowledge points required by the two questions could all be applied to physics.
The former is widely used in physics, and the latter is related to quantum theory and system dynamics, and they are all knowledge points that he still has in his memory. There is no need to stay up late tonight and read books to revive these two pieces of knowledge. .
"Brother Chuan, can you do it?"
Suddenly, the corpse-like Lu Tianrui ejected over and asked urgently.
"It's okay, it should be possible to solve it." Xu Chuan replied, staring at the manuscript paper. As he spoke, he began to answer the question on the manuscript paper.
"First transform this inequality into ab(a-b)+bc(b-c)+ca(c-a)=-(a-b)(b-c)(c-a)(a+b+c)."
"Then let a-b=x, b-c=y, c-a=z, a+b+c=s, then"
"Next, twist the original inequality into M(x+y+z+s)≥9|xyzs|(x+y+z=0)"
"By this point, you should know what to do next."
"Gan! Even if I'm not as good as you in physics, math is my strength!"
Looking at the transformation inequalities that Xu Chuan had listed on the manuscript paper for a while, Lu Tianrui suddenly wailed, attracting the attention of others in the classroom.
A question that he couldn't find a way to solve in a short period of time was actually solved in Xu Chuan's hands?
Was he originally engaged in physics or mathematics?
Why are you so perverted?
Suddenly, Lu Tianrui seemed to have thought of something, and reached out to take the draft paper on Xu Chuan's desk that he had used to solve the problem.
When he saw it, he was once again stunned by the calculus formulas.
"Use calculus to solve the slope of the curve, Brother Chuan, you are awesome! Why didn't I think of it?"
Lu Tianrui murmured to himself, staring at the answers on the scratch paper and lost in thought. There is no doubt that Xu Chuan's problem-solving method opened up a new mind for him.
After staring at the manuscript paper in his hand for a long time, suddenly, the little round face came over again.
"Brother Chuan, tell me about your problem-solving ideas in analytic geometry, and how to find the limit. Can it also be done using integrals?"
Hearing this, Xu Chuan looked at the little fat man strangely. He understood a little bit how Teacher Gong felt before.
It is clear that the limit of the second question must be solved with Lupida, and this is the easiest solution. There are simple ones that are not used, but complex ones must be used. Is this a brain problem?
But since he asked, Xu Chuan looked at the question again, thought for a while, and replied: "Calculus is not good. It should be possible to solve the limit of definite integrals, but you have to convert the question into definite integrals first, and then ”
After a while, the excited eyes of the small round face were blurred into slits.
"I understand! Brother Chuan!"
The hour and a half of evening self-study passed quickly. Gong Rihui collected the answers on time and looked through them one by one.
Although the questions were selected from various competition textbooks, they had also undergone his own changes. He knew the answers and solutions to these questions very clearly. He could tell right from wrong at a glance.
Suddenly, a somewhat familiar disintegration method and answer came into his eyes. When he saw the name, it was Lu Tianrui.
"Lu Tianrui, where did your idea of using definite integrals to find the limit come from? What you learned is neither fish nor fowl! And you did it all wrong! The more you learn, the more you fall back! If this continues, are you still going to participate in a p-number competition?"
On the podium, Gong Rihui, who had just read the solution to the problem and was familiar with the answer, angrily smashed a half-broken piece of chalk directly onto Xiao Yuan's head.
This familiar method seems to have just been learned from Xu Chuan's problem solving, but this guy's foundation in integral calculus is not that solid. It is not impossible to find the limit with definite integrals, but it has a range of applications, and this thing has changed. When calculating the points, the transfer went directly to the wrong point.
"Also, Xu Chuan, sit in that seat and don't stay around him. You'll lead me to bad guys as soon as you come."
Suddenly, Gong Rihui pointed his finger at Xu Chuan, pointed angrily at the seat on the other side of the classroom, and asked him to sit there.
This kid has ruined Lu Tianrui's life in just one day. If he works hard for a few more days, Lu Tianrui won't even have to participate in IMO.
Xu Chuan looked innocent, turned to look at the fat man next to him, and silently changed positions.
(End of chapter)