I really just want to be a scholar

Chapter 4 What kind of fairy topic is this?
After a while, Lao Zheng came back to his senses, handed over the chalk and said, "You write down the process of solving the problem."

Qin Ke started writing in a hurry.

"(1) Because F(c, 0), A(a, 0), B(0, b), C(0, -b),

So the equation of the straight line AB is x/a+y/b=1,

The equation of straight line CF is x/c-y/b=1,

……

所以椭圆E的标准方程为x^2/4＋y^2/3＝1”

"(2) Suppose there is a straight line l, so that F is the orthocenter of △BMN, connect BF, and extend, connect MF, and extend, as shown in the figure, then BF⊥MN, MF⊥BN,

......"

The students in the audience were stunned.

"Fuck, this answering process is a bit brain-intensive, I can't understand it..."

"Why doesn't Teacher Zheng say a word, and doesn't comment on one or two?"

"Call the math rep and see if this guy is doing it right?"

"Don't ask the department representative, he's still staring at you if you don't see him? You should ask Ning Qingyun, the school committee."

A female student at the front desk hurriedly turned her head and asked Ning Qingyun, "School Committee, did Qin Ke do the right thing?"

Ning Qingjun looked at the figure writing on the podium with a complicated expression, and nodded: "So far, it's all right."

The whole class suddenly went into an uproar.

Ning Qingyun's status as a super student is well known in Yingyuan High School, so although they have only been in the same class for about two months, in the hearts of the students, Ning Qingyun's words can basically be equivalent to the teacher's words, The school committee said it was right, and it was right!
The question is, is this Qin Ke's math level really so high?Or have you been hiding your strength before?
At this time, Qin Ke had finished writing the answer process, but saw that he drew a long dividing line under the final answer, and then started writing again.

"What is he doing... Fuck! 'The second solution', he is going to use the second solution!"

"Really? Is there a second solution to this question?"

"No... this is not finished yet, he wrote 'the third solution'... I am not dazzled, am I? Is this the last five words he wrote?"

Under countless surprised and even dull eyes, Qin Ke used three different solutions to solve this problem. After writing, he threw away the chalk and returned to his seat gracefully.

quiet!There was silence in the whole classroom.

Everyone stared dumbfounded at the blackboard full of answers, and couldn't believe their eyes.

Ordinary students can't even fully understand these three different solutions. Only seven or eight top students with good math scores can tell that all three solutions are correct!

All of a sudden, everyone looked at Qin Ke with incredulous eyes.

If only one of the solutions is written, it can be said that you have seen similar problems somewhere, but it is hard to say that the three different solutions are fooled.

Ning Qingyun looked at Qin Ke in surprise again, her pretty face couldn't hide her surprise.

Because even she only thought of two solutions just now, and she didn't have time to write them out to verify, but the guy in front of her who slept in class and handed in a blank paper in the monthly exam, unexpectedly wrote three different correct solutions easily?
Especially the last solution, even she thought for a while before she understood it.Because it uses the plane curve polar coordinate equation in the mathematics elective 6 textbook, it is not something that students who have only completed half of the last semester of the second year of high school can master.

Could it be that this Qin Ke, like her, has taught himself all the content of high school mathematics?The most incredible thing is that this guy gave the correct answer as soon as he opened his mouth just now. Could such a question be solved by mental arithmetic?
Is this really the same person as the problem student in her impression, the scumbag who handed in blank papers?
Ning Qingyun was a little flustered.

It was Zheng Jianzhou, the math teacher, who was most surprised and even pleasantly surprised. He carefully read the three solutions line by line, and then suppressed his excitement and said: "These three solutions are all correct. One solution, I didn't expect Qin Ke to think of three solutions in one go, Qin Ke's math level is really good!"

He didn't talk about Qin Ke's mental arithmetic, because he was afraid of scaring ordinary students.He had a vague premonition that this kid might be the hidden math genius he had been looking for!Always with double standards, he looked around the audience without hesitation and said, "Boys in the class, you all sincerely apologize to Ning!"

The 37 male students looked at me, and no one dared to renege on Lao Zheng's terrifying pressure. In desperation, they had to stand up and shouted together: "Student Ning Qingyun, I'm sorry!"

Ning Qingyun's face was a little red, and she glanced at Qin Ke who was humming next to her. She didn't know what it was like, so she blushed and whispered, "It's okay...it's okay."

Zheng Jianzhou signaled the male students to sit down: "I won't explain this question. Qin Ke's solution is written in detail. You can just read the steps to solve the problem by yourself. If you don't understand, you can ask Qin Ke after class."

Qin Ke listened happily to the continuous system prompts:

"Ding! The host has gained double the shock value of 102 points! The experience value of learning the gods +102."

"Ding! The host has gained 32 points of jealousy! The experience value of the god of learning +32."

"Ding! The host has gained 49 points of envy! The experience value of the god of learning +49."

He didn't care about the eyes of others and what Old Zheng said on the stage. He was only thinking in his mind that the wave of pretentiousness just now should have earned almost 500 experience points for the mission target, right?
As expected, he soon heard a new system beep:

"Ding dong! Congratulations, you have completed the 'new function task: Pretending to make me progress', and the rewards are being distributed... Your experience of learning the gods is +1000!"

"Ding dong! Congratulations, your god of learning experience has accumulated to 2100 points, which makes your math level upgraded to: 'High School Math Olympiad (city-level preliminary competition) level'. So far, any math questions that do not exceed the difficulty of the municipal-level preliminary competition It’s no longer difficult for you, you can even calculate the answer directly in your head.”

"The next level of Mathematics: 'High School Mathematics Olympiad (Provincial Rematch) Level', you need to accumulate 5000 points of academic experience. Please continue to work hard!"

Qin Ke clenched his fist excitedly, yeah!The math level has improved again!Countless knowledge and experience of the Olympiad poured into Qin Ke's brain. Qin Ke even felt that his brain became clearer, and Esprit became more agile and flexible. The biggest evidence was that he digested the new knowledge and experience of the Olympiad from the system. It took less than 1 minutes.

Suddenly I heard Zheng Jianzhou say: "Qin Ke, come up and do these two questions again."

If someone pays attention, they will find that Lao Zheng's tone is extremely gentle, not as blunt and forceful as he usually treats students.

Qin Ke was delighted, when he heard Lao Zheng calling him, he looked up at the newly written question on the blackboard, and saw that it was a proof question, and the question was only a short sentence, to prove an inequality, but the more Simple questions are harder to prove, especially quadratic inequalities in one variable are compulsory 6 knowledge points.

But for Qin Ke, he can understand the train of thought and the answer after a little thought.

He walked to the blackboard, picked up the chalk and brushed it, and directly used the function extremum method to make it easily.

There was another exclamation from the audience, and Qin Ke's ears kept ringing the system's prompt sound, like a fairy sound, so when Lao Zheng asked him to do another question, Qin Ke looked at the funny three hairs on his head. Feeling pleasing to the eye, he immediately said cheerfully: "Come on, just let the horse come over!"

The corner of Zheng Jianzhou's mouth curled up into a meaningful smile, and he wrote the last question:

"Prove: Among any 6 people, either 3 people know each other, or 3 people don't know each other."

This time it was Qin Ke's turn to be stunned.

Not only Qin Ke, but even the whole class were stunned.

What kind of fairy topic is this?
"...Is Mr. Zheng asking a math problem? I feel like I'm in a fake school. Why do I know all the characters, but I don't understand it at all?"

"That's right. I think the first three questions are difficult enough, and this question is even more clueless. How can I prove it? Get six people to ask it?"

"If there are six random people, all six students in the class know each other, right? Is this a proof?"

"You are stupid. There is an 'or' in the title, which means that both cases must be proved. No, it is proved separately or at the same time. I am confused by myself. What a fairy question!"

"Qin Ke is afraid that he won't be able to solve it this time? Seeing how frightened he is, why don't you just let the horse come here!"

The audience was chaotic, and most people didn't understand how difficult this question was. They only thought that Qin Ke might not be able to solve it, so they subconsciously became happy.

No one would be happy to see a scumbag who goes to class and sleeps every day suddenly rises up. Even if they can't do it themselves, it still doesn't prevent them from gloating. This proves that although Qin Ke is a bit powerful, he is no better than them How powerful is it.

Only Ning Qingyun frowned, subconsciously worried for Qin Ke, because she knew very well that this was an Olympiad problem!The difficulty is so high that even she is not sure that she will be able to solve it!
This Qin Ke has never read books on Olympiad, so how could he do it?
Under the gazes of countless people, Qin Ke said: "Teacher, did you make a foul? This is not a subject for high school exams."

To come up with such an over-the-top question, and let people pretend to be pleasant?If I hadn't just raised my math level, I would have been stumped by this question.

All the students breathed a sigh of relief, Qin Ke really wouldn't!
A trace of disappointment also flashed in Zheng Jianzhou's eyes: "Why, you can't solve it?"

Unexpectedly, Qin Ke just said "hehe" twice: "It's not bad, such a topic is a bit interesting to do."

He picked up the chalk and said: "We can turn this proof problem into a proof of the famous Ramsey-type problem in graph theory, that is, to prove that there must be triangles of the same color in a 2-color complete graph K6."

Zheng Jianzhou's eyes lit up again: "You actually know graph theory and Ramsey-type problems?"

"Common question types in Mathematical Olympiad." Qin Ke said and drew six points with chalk:
"Suppose six people are A1, A2, A3, ..., A6, if they know each other, they will be connected by a red line, and if they don't know each other, they will be connected by a blue line. gone."

The small question marks on the faces of the students in the audience: "???"

what are you saying?Why do I understand everything you said, but I just don't understand how to solve the problem?And who is Ramsey?Are there other gods of mathematics besides Gauss in the world?
Qin Ke connected the dots with red and blue chalk respectively, and said: "A1 can have five sides, A1A2, A1A3, ... A1A6, according to the drawer principle, there must be three sides of the same color."

Students in the audience, you look at me, the principle of the drawer?What the hell?Can you speak human words!

“我们先假设A1A2，A1A3，A1A4是红边三角形，那么若是△A2A3A4为蓝边三角形，那么结论可证；如果△A2A3A4有一条红边，我们以A2A3为例，可以看到，如果A2A3为红色，那么△A1A2A3为红色三角形，结论依然可证。”

Except for Ning Qingyun and a few top math students who had studied Mathematical Olympiad, most of the students in the audience still looked dumbfounded.

"Hey, does anyone understand what Qin Ke is talking about? It seems that what he said is very simple, why do I seem to be listening to a scripture and can't understand at all?"

"What does he mean by that, the proof is over?"

"It turns out that I'm not the only one who can't understand, so I'm relieved."

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(End of this chapter)