A genius? I just love studying.

Chapter 17 Is He a Devil?

As soon as they thought of this, the looks in the students' eyes when they looked at An Chengzhang and Chen Hui suddenly changed subtly.

Perhaps, as that classmate said, since it is cheating, the answers can be memorized, and the problem-solving process can naturally also be memorized.

In their opinion, someone who could solve the previous difficult problem should not be stumped by this simple one.

and so……

Not only the math competition team members, but the students outside the classroom also had strange expressions.

They really didn't know the answer to this question, but judging from the conversations and expressions of the math competition team members, this question was not difficult, at least not more difficult than the one Chen Hui had just solved.

But Chen Hui couldn't solve such a "simple question".

What this shows is self-evident.

The smile on Yu Chuhao's lips was almost gone, and he was screaming madly in his heart.

Even he himself didn't expect that he actually made the right bet!

This Chen Hui is indeed a fake!

How could a person who usually scores over 80 in math possibly beat a bunch of math competition team bosses?

As a result, when I encountered a question that I had not memorized, my true colors were immediately revealed.

Tan Junjie's complexion had returned to normal at this time.

The other team members knew how to do this question, so he naturally didn't find it difficult.

Seeing Chen Hui's helplessness, he suddenly realized that the method of solving the problem is not important, as long as he can do it, it is enough.

So it’s no big deal that Chen Hui can solve the problem with junior high school knowledge. He can also solve it, and he is taking the right path.

Look, when faced with this problem, Chen Hui had no weapons in his arsenal and was also helpless, but he was able to solve it.

He is no worse than Chen Hui!

How could he be worse than Chen Hui!

Only Liang Peixuan suddenly thought of something.

He had just joined the Math Competition Team for less than a month, and this was the time when he felt the gap between Math Competition Team members and ordinary high school students most deeply.

The other team members were used to this question, but he was the only one who knew that if he had not learned the problem-solving methods for the competition, he would also be helpless if he encountered this question.

He stood up quietly and wanted to say something, but for a moment he didn't know what to say.

Time passes minute by minute,
"Okay, this question is indeed a bit difficult."

Zhang Anguo came to Chen Hui and said, "You have some talent in mathematics, but you are still a long way from being able to compete. Give up..."

However, before he finished speaking, Chen Hui suddenly turned around and picked up the chalk on the desk.
Duoduoduo wrote a formula on the blackboard.

a^2b(ab)+b^2c(bc)+c^2a(ca)=a(bc)^2(b+ca)+b(ab)(ac)(a+bc)
"???"

Zhang Anguo's words came to an abrupt halt as he looked at the formula on the blackboard, confused.

He was the one who set the problem, so of course he knew the correct solution.

At least it has nothing to do with this formula.

Chen Hui didn't see Zhang Anguo's expression. He continued to write with chalk. It was known from the question that a≥b≥c≥a, and the circular permutation of the size relationship did not affect the inequality.

Therefore, a(bc)^2(b+ca)+b(ab)(ac)(a+bc)≥0.

The equality holds if and only if a=b=c.

Chen Hui didn't know what Zhang Anguo was thinking. He just finished writing the proof and looked back at Zhang Anguo.

As if struck by lightning! Zhang Anguo understood Chen Hui's proof.

He has been studying high school math competitions for some time and has some level of experience.

But the key is, who can tell him where the equation on the right came from?

Without checking, he knew that the formula should be correct. This was his intuition as a mathematician.

But he had no idea how to convert the equation on the left into the equation on the right. Even in mathematics there was no such method, at least not even he, a teacher who had studied mathematics for decades, knew it.

The conventional approach to this problem should be to use the substitution method to reconstruct the formula and obtain the inequality relationship.

Use the inscribed circle to divide the triangle into three pairs of six equal sides, and convert a, b, and c into expressions of x, y, and z.

Substituting xyz into the original formula, we can obtain x^2/y+y^2/z+z^2/x≥x+y+z (1). According to the Cauchy-Schwarz formula, we can obtain (x^2/y+y^2/z+z^2/x)≥(x+y+z)^2. Since x, y, z＞0, formula (1) holds.

According to the conditions for the equality of the Cauchy-Schwarz formula, we can know that when a=b=c, the equality of the original inequality holds.

Therefore, the students in the mathematics competition team all thought that this problem was not difficult, because the difficulty of this problem lies in knowing that the trigonometric inequality needs to be proved by the substitution method, and at the same time, one must know the technique of substitution. After that, it is just a slightly tedious calculation. As long as the final inequality is obtained, the Cauchy-Schwartz formula must be known to all high school students, so it is naturally not a difficult problem.

However, Chen Hui actually transformed the original inequality into an extremely concise formula directly through algebraic operations, so concise that people can see the conclusion at a glance.

It is indeed necessary to use the construction method to solve this problem, but the construction method that everyone knows is completely different from the construction method you use!

What's the difference between directly constructing an equation to draw a conclusion and rubbing an atomic bomb with your hands?
How did he do that?
How is this different from Einstein guessing the formula of general relativity from experimental data?
What kind of monster is this?

Zhang Anguo had no idea how many times he had asked this question in his mind.

He picked up the chalk and began to calculate on the blackboard. Although he intuitively felt that there was nothing wrong with the formula, the rigor of being a mathematician made him decide to calculate it again.

Of course, he still felt a little unwilling.

In the classroom, Tan Junjie had already started calculating on his scratch paper as soon as he saw Chen Hui write out the formula. The formula was not complicated, and he got the result quickly.

The equations on both sides are equal!
"What kind of monster is this man?"

Tan Junjie looked at the draft paper, his eyes a little out of focus.

The two questions today had a huge impact on his view of mathematics. He felt that the mathematics he had studied for more than ten years seemed to be a wrong path.

The other members of the Math Competition Team were also somewhat bewildered.

Chen Hui's proof process was very simple and they could understand it.

But how was that devilish formula solved?
They racked their brains but couldn't figure it out.

At this moment, they also had the same doubts and confusion as Tan Junjie.

It's like a Huashan disciple who has studied swordsmanship for a lifetime and thinks he can dominate the world with his superb swordsmanship. Unexpectedly, one day someone comes to challenge him. This person's swordsmanship is mediocre, but every move is deadly, leaving them without any chance of defense.

They can't help but question their own path.

It must be fake, right?
They looked at Zhang Anguo who was calculating on the blackboard, as if they were grasping at the last straw.

They actually had a huge desire in their hearts, hoping that Chen Hui's formula would be wrong.

Liang Peixuan, who was originally preparing to say something to help Chen Hui out of the predicament, stood in his seat, staring blankly at the blackboard, with mixed feelings in his heart. He did not follow the calculation.

There is no need for that anymore.

Zhao Defeng stared at the blackboard intently, watching Zhang Anguo's calculations. He hadn't touched mathematics for many years, but now he was also thinking along with Zhang Anguo's calculations, fearing that Zhang Anguo had made a mistake somewhere.

The joy in Yu Chuhao's heart shattered like bubbles. He felt as if a basin of cold water was poured on his head, which made him shudder and become energetic.

He also looked at the blackboard nervously and started to calculate with Zhang Anguo.

The students outside the classroom looked confused, not knowing what was going on.

It seems that Chen Hui has already proved it?
Why is everyone reacting like this?
(End of this chapter)