Great Country Academician

Gong Rihui frowned fiercely, feeling that this kid was pretending to be beta, but he couldn't say anything, after all, the reason was quite 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 must keep this kind of problem-solving thinking, but you can't just because Be different and forget 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 seen since teaching, and it would be a waste not to learn mathematics.

Maybe this competition is an opportunity. If you teach him well, he may be able to break him into mathematics. After all, he is only seventeen years old, and it is not too late to start learning.

"Advanced algebra, differential geometry, partial differential equations, and ordinary differential equations are almost all finished."

Xu Chuan picked some university mathematics answers for studying physics.

Although the mathematics he has learned is definitely more than these, but those deeper things and mathematics that are not used in competition with things are obviously not suitable for speaking now.

"Oh? Then I'll give you another debut question."

Gong Rihui was a little surprised. He didn't expect this kid to have read so many college mathematics, which is comparable to the students who can enter the national team.

He casually took a piece of draft paper and a pen from Xu Chuan's desk, and sat down on the desk beside him.

A quarter of an hour later, a piece of manuscript paper with two questions returned to Xu Chuan's desk.

"Give me the answer tomorrow."

After speaking, Gong Rihui returned to the podium and continued to drink tea, read newspapers and fish.

"Show me, show me, Brother Chuan."

Next to him, Lu Tianrui with a round face came over curiously. Although he hadn't finished the two questions on the blackboard, it didn't affect him at all.

After grabbing the manuscript paper from the table, Lu Tianrui couldn't wait to read it, but the next second, he began to doubt his life.

1. Find the smallest real number M such that the inequality holds true for all real numbers a, b, and c

|ab(a-b)+bc(b-c)+ca(c-a)|≤M(a+b+c)

two,.

The first question caught his eye, but Lu Tianrui was a little dumbfounded before he read the second question. He couldn't find a place to start with an inequality in the first place.

How to find the minimum real number M?

First change the formula so that both sides are equal? Or preconditions? Doesn't seem to work?

After studying for a while, he still couldn't think of a way to start solving the problem, he lay down on the chair, stared at the ceiling silently, and began to doubt life.

"Is it that difficult?"

Xu Chuan took the manuscript paper with some curiosity, and the topic was snatched away before he read it. Will this force a math genius to shut himself up?

"One way to find inequality and one matrix, it seems quite interesting."

Xu Chuan stared at the two questions. The knowledge points required by the two questions can be applied to physics.

The former is widely used in physics, while the latter is related to quantum theory and system dynamics, and they are all knowledge points that he still has memory. There is no need to stay up all night to read the book to recover the knowledge of these two pieces. .

"Brother Chuan, can you do it?"

Suddenly, the corpse-like Lu Tianrui shot over, asking urgently.

"It's okay, it should be solved."

Xu Chuan stared at the manuscript paper and replied, while talking, he began to answer 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)"

"At this point, you should know what to do next."

"Hey! I'm not as good as you in physics, but mathematics is my forte!"

Seeing Xu Chuan list the transformation inequality on the manuscript paper for a while, Lu Tianrui suddenly wailed, which attracted the attention of other people in the classroom.

A question that he couldn't find a way to solve in a short time in Xu Chuan's hands was actually solved?

Did he study physics or mathematics?

Why are you so perverted?

Suddenly, Lu Tianrui seemed to think of something, and reached out to take the draft paper on Xu Chuan's desk that he had previously solved.

After entering his eyes, a piece of calculus formula made him stunned in place again.

"Use calculus to solve the slope of the curve, Brother Chuan, you are amazing! Why didn't I think of it?"

Lu Tianrui muttered to himself, staring at the answer on the draft paper and fell into deep thought. Undoubtedly, Xu Chuan's problem-solving method opened up a new brain hole for him.

He stared at the manuscript paper in his hand for a while, and suddenly, Xiao Yuanlian entangled him again.

"Brother Chuan, tell me about your problem-solving ideas in analytic geometry, and this way of seeking the limit, can you also use integrals to do it?"

Hearing this, Xu Chuan looked at the little fat man in a strange way. He understood what Teacher Gong felt before.

The second problem of finding the limit clearly needs to be solved by L'Hopital, and this is the easiest solution. If there are simple ones, don't use them, but if you have to use complicated ones, is there something wrong with your brain?

But since he asked, Xu Chuan looked at the question again, thought for a while, and replied: "Calculus is not good, the limit of definite integral should be able to be solved, but first the question must be converted to definite integral, and then "

After a while, Xiaoyuan's excited eyes were blurred.

"I understand! Brother Chuan!"

An hour and a half of evening self-study passed quickly, and Gong Rihui collected the answers on time, flipping through them one by one.

Although the questions are selected from various competition textbooks, they have also undergone his own changes. He is very clear about the answers and solutions to these questions, and he can know right from wrong with a glance.

Suddenly, a seemingly familiar disassembly method and answer came into his eyes, and he saw the name, Lu Tianrui.

"Lu Tianrui, where did you come up with the idea of ​​using definite integrals to find the limit? What you learned is neither fish nor fowl! You made mistakes! The more you learn, the more you regress! If this continues, you still participate in a p math competition?"

On the podium, Gong Rihui, who had just finished reading the solution and was somewhat familiar with the answer, angrily threw a half-broken piece of chalk directly on Xiaoyuan's face.

This familiar method looks like it was just learned from Xu Chuan's problem solving, but this kid's foundation in calculus is not that solid. When the integral is determined, it is directly transferred wrong.

"Also, Xu Chuan, sit in that seat, don't stay by his side, and bring bad guys to me as soon as he comes."

Suddenly, Gong Rihui pointed at Xu Chuan, pointed to the seat on the other side of the classroom with an angry hand, and asked him to sit there.

This kid has brought Lu Tianrui to his knees after only one day. After a few more days of tossing around, Lu Tianrui won't have to participate in the IMO.

Xu Chuan looked innocent, turned his head to look at the little fat man beside him, and silently changed his position.