What the?!

Hearing what Zhang Hao said, everyone, including Liu Yingtian, was stunned, thinking that they had heard it wrong!

"What are you kidding? That waste can solve this problem?!" Liu Chao said very loudly there:

"If you can solve it, I, Liu Chao, stripped naked and went to the playground to run naked!"

"Will you solve it?!Don't laugh at other people's big teeth, okay?!" Xie Ziming also said with disdain.

"Get out of the way, I'll let you see what a real god of learning is today!" Ignoring the skeptical eyes of a group of people, Zhang Hao walked directly onto the podium and pushed Xie Ziming aside.

Zhang Hao is very confident. Because he just added a sentence to himself on the Chaos All Souls List: "On November 18, 218, the god of learning possessed!"

Xie Ziming was pushed away by Zhang Hao, very unhappy, but there was no way, after all, he couldn't beat Zhang Hao.

Therefore, he could only snort coldly there: "Pretending, it will take me a lot of time to solve this problem, and you can solve it even if you are the penultimate one?"

Liu Yingtian's question was originally deliberately difficult, because this kind of question generally appears in the finale of mathematics in the college entrance examination, and few people can easily solve it, but this is nothing to Zhang Hao, who has learned to be possessed by God.

"Brush, brush, brush!" Zhang Hao finished answering in a while. The whole process is smooth and smooth in one go.

Liu Yingtian glanced at it casually and sneered: "Look at what kind of mess you wrote? With a dead mouse in your waist, pretending to be a hunter, don't be ashamed here!"

Upon hearing this, the whole class burst into laughter.

"No, wait!" Liu Yingtian's eyes suddenly widened: "Can this problem still be solved in this way?"

When everyone heard it, they all looked at it curiously, but when they looked at it, they were confused, and they only felt that one head and two were big, because they didn't talk about Zhang Hao's problem-solving method, and they hadn't even heard of it!

The title on the blackboard is: Proof X-1/6X³≤sinx(x≥)

Zhang Hao's solution is: from the meaning, the left side is the elementary function of the cubic binomial, the right side is the trigonometric function, and there is no obvious size relationship between the two sides.

The second-order McLaughlin's formula for sinx at x= is denoted as f(x)=sinxﾗx+1/6x³，f()=，f′(x)=cosxﾗ1ﾑ1/2x²=，

f″(x)=-sinxﾑx,f″()=，f″′(x)=-cosxﾑ1，f″′(ζ)=-cosζﾑ1,

When n=3, the Taylor expansion of f(x) is: f(x)=ムムム1/3!(1ラcosθx)·οx³,

From the above, f(x)=1/6(1ラcosθx)·x³ムο(x³)≥(x≥,ζ≤θx,ニψニ1),

So when x ≥, there is x-1/6x³≤sinx.

"Isn't this question still going to be graphed, and the corresponding arc length of the angle in the unit circle is compared with its sinusoidal sinx?" Xie Ziming looked at the delicate and powerful white font on the blackboard, and sneered disdainfully:

"Just write a few formulas and just want to fool the past? I am an idiot and treat others as idiots!"

But Liu Yingtian was stunned there, Zhang Hao's solution did not have any problems, and it was even beyond his imagination.

After a long time, Liu Yingtian came back from the shock, and looked at Zhang Hao differently:

"How did you come up with the idea of using the McLaughlin formula and the Taylor formula. The high school curriculum doesn't have any of that, how do you know that?"

This problem originally took many steps to solve, but Zhang Hao skillfully and directly used a higher-level formula to solve it in three or two steps!

To be honest, Liu Yingtian also knew Taylor's formula and McLaughlin's formula, but he never thought of using these two formulas to solve this problem, and Zhang Hao, who he always thought was a waste, actually did it!

How is this possible?!

When Xie Ziming heard this, he was stunned for a moment. Listening to the meaning of Mr. Liu's words, it seems that Zhang Hao's solution is not only correct, but also uses a higher method that even he has never heard of?

How could that shit have a mathematical formula that he didn't even know?!

"Self-taught!" Zhang Hao replied lightly, he is now learning to be possessed by God, even if he can solve difficult problems, what is this high-level mathematical formula?

"Are you teaching yourself advanced mathematics?!" Liu Yingtian was stunned, and then snorted coldly that he couldn't get off the stage:

"I haven't learned to climb yet, I want to learn to walk. I didn't even learn math in high school, so I went to study more advanced courses on my own, which is too incomprehensible, right?"

"What does the teacher mean, do you think your math level is higher than mine, and I have to study hard with you?" Zhang Hao asked with some amusement.

"Nonsense! Am I a teacher or are you a teacher? Don't think you're great just because you've learned a little bit of advanced math!"

Liu Yingtian glanced at Zhang Hao unhappily, thinking that the latter was just a fluke, and he just happened to learn advanced mathematics.

"Then I would like to ask Mr. Liu, in the mathematical community, who is generally believed to be the founder of matrix theory?"

"Of course it's Kailai!" Liu Yingtian raised his eyebrows proudly, this was not difficult for him!

"Well, Gloria once had a corollary that the product of two matrices can be zero, and it doesn't need one of them to be zero, but only one of them is indefinite, do you think this inference is correct?"

Zhang Hao opened his mouth and came, and the classmates in the audience were stunned. What Gloria? What matrix? I've never heard of it!

"Of course it's true, that's an indisputable fact in the world of mathematics!"

Liu Yingtian was shocked at first, shocked that Zhang Hao actually knew that the matrix theory was still the same one who slept all day. Isn't Zhang Hao, a waste who doesn't learn and doesn't have skills?

Then he breathed a sigh of relief, fortunately he had learned about this before, if he changed to another math teacher, he would definitely be stumped!

Zhang Hao was also a little surprised, although Liu Yingtian's character is not good. But I know a lot.

But that's not all!

"Actually, Gloria is wrong, this inference is wrong, because in this inference, the two matrices must be indefinite, and the product of the two matrices can be zero!

Zhang Hao smiled faintly, and didn't wait for Liu Yingtian to react. He went on to ask:

"Weierstrass was the first to get the standard type of beam aλb, how do you understand the standard type of this beam?"

"A and b here are not necessarily symmetrical, but obey the condition that the absolute value of aλb is not constant equal to zero!"

Liu Yingtian is also the leader of the mathematics group no matter what he says, and he answered with a relaxed face.

But no one knows how big the shock in his heart is?! This Zhang Hao actually has such an unpopular mathematical knowledge?

"Very good, but although this condition is proved by Weierstrass, its inverse theorem comes from Sylvester, and some scholars have written a sentence about this inverse theorem, do you know what it is?"

"I... I don't know..."Liu Yingtian was really stunned this time, what kind of demon is this kid he has always been optimistic about, how can he even know this?

The students in the audience were also stunned, Zhang Hao actually stumped Mr. Liu, the leader of the famous mathematics group of Xinhua No. 1 Middle School? !

You must know that Liu Yingtian is still the teacher of the marking group of the annual college entrance examination, although the teacher's morality is not good, but his achievements in mathematics teaching and research are still very good.

Wang Shiyu and He Jing looked at it with their chins propped up below, their eyes were full of little stars, Zhang Hao had an inexplicable attraction when he asked questions, it was an invincible confidence!

"Then I'll tell you. This inverse theorem says that if the determinant of aλb is consistent with the elementary factor of the determinant of aλb, then a pair of linear transformations can be found that change a to a and b to b at the same time. Teacher, how do you understand this inverse theorem?"

Zhang Hao didn't mean to stop at all, but spoke again like a cannon.

"I... I can't understand..."Liu Yingtian was completely stunned, seeing that his forehead was already covered with fine beads of sweat, and he didn't know how to answer.

"Then teacher, do you have any questions?" Zhang Hao smiled faintly. Fight with me, you old man is still far away!

"It's gone.. Right..."Liu Yingtian lowered his head with a red face, and said with a weak heart.

He never dreamed that he would be dumbfounded by his own students, the key is a student he always thought was rat!

"No problem, I'll continue to go back and discuss life with my sister, and ask me if there is anything that won't come back in a while!"

Then, Zhang Hao said something lightly, and walked back to his seat with a swagger.

As soon as these words came out, the whole class was stunned. Zhang Hao's words are too arrogant, isn't this a slap in the face of Mr. Liu, who knows what the latter will be angry?

A group of people turned their heads, and sure enough, they saw that Liu Yingtian was already angry. It's about to explode.

"It's over, dare to make the head teacher so faceless, Zhang Hao probably won't be able to mix in this class in the future!" Although He Jing admired Zhang Hao's domineering, he could only lament.

"Hmph! I really thought it would be great to be able to solve a problem! Look at how Mr. Liu will clean you up in a while?!" Xie Ziming and Liu Chao snorted coldly, their eyes full of schadenfreude.

Soon, Liu Yingtian broke out directly, only to see the green tendons on his hands and neck burst out, and he roared hysterically: "Zhang Hao!!!!"

......

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