Xueba, I beg you to go and escort him quickly!

已知F1,F2分别为双曲线C：（x2/9）-（y2/27）=1的左右焦点，点A的坐标为（9/2，根号下135/2），则∠F1AF2的平分线与轴的交点M的坐标为多少？

"Hiss... what kind of topic is this..."

Look again!

Let f(x)=x2+bx+c, if the equation f(x)=x has no real roots, then the equation f(f(x))=x(?)

"My God, what is this and what! I can't understand it at all..."

All of the above are multiple choice questions!

Yue Pingting didn't even look at the options, because the topic alone made her one head and two big!

"I don't believe it anymore!"

Look at the fill in the blank question again.

It is known that (1-丨cosx丨)/(1+丨cosx丨)=sinx, then x=?

Yue Pingting is not feeling well...

She doesn't want to watch it anymore.

The multiple-choice questions and fill-in-the-blank questions were enough for her to give her a headache, and she dared not read the questions that followed.

"Give it back to you! Give it back to you! Hiss..."

Yue Pingting's scalp was numb.

"Now I know the gap!"

"Yang Kaixuan, come on!"

Yang Kaixuan, "..."

As the school bell rang.

Yang Kaixuan started his own "Olympiad" preparations.

Start with one question after another.

It was a bit jerky at the beginning, and it took a long time to do the questions, but it got better later on.

After all, he has a strong foundation, and he has considered this aspect before, so he is prepared.

But he is not good at any topic!

A test paper, if it is an ordinary test paper, even if it is a college entrance examination paper, he will not have so much space!

But on this test paper, most of Yang Kaixuan left blank.

For some topics, it’s one thing that he doesn’t understand, but it’s another thing if he understands it and starts to do it!

difficult!

It's so hard!

He turned his head and glanced at Xu Heng.

He was watching the drama with headphones on, and he couldn't help laughing.

"Ahem! Well, Xu Heng...Xu Heng, this question...' 々..."

Yang Kaixuan pointed to this question.

topic:

Knowing x∈R, what is the value of (x(x+1))+arcsin ((x2+x+1)) under the root sign?

Xu Heng lingered on this question for a few seconds, then picked up his pen.

Rarely!

He picked up the pen and wrote and drew on the paper...

But there was not even a minute, Xu Heng said lightly: "π/1."

He didn't even give Yang Kaixuan a chance to ask why.

Xu Heng handed him what he had just written.

solution:

因为x2+x≥0，所以x2+x+1≥1，从而x2+x=0，所以原式=π/2。

It's that simple!

Yang Kaixuan didn't dare to breathe.

"This..."

He is in shock...

Haven't responded yet.

Xu Heng thought he had other problems, so he took another look.

topic:

设x＞0，则f（x）={（x+1/x)4次方-（x4次方+1/x四次方）}/{（x+1/x)3次方-（x3次方+1/x3次方）}的最小值为多少？

Xu Heng took back the papyrus from Yang Kaixuan and started writing.

Yang Kaixuan, "???"

He was puzzled, but he still leaned over to follow.

令t=x+1x，则t≥2，x4次方+1/x四次方=t4次方-at2+2x三次方+1/x三次方=t次方-3t，所以f（x）=g（t）=（4/3）t-(2/3)t-1方……

……

"The last is equal to f(1), so the minimum is 7/3."

Yang Kaixuan was dumbfounded.

Although I finally saw that Xu Heng used the acting straw, but what was written on the acting straw was for the convenience of Yang Kaixuan to understand clearly.

"Um...Xu Heng, let me ask you a question...if you don't write it down for me...wouldn't you...could you figure out the answer?"

Xu Heng shook his head, "No, no, how can it be possible to calculate by mouth, you can see that it is impossible to do it by mouth!"

Yang Kaixuan breathed a sigh of relief, "Huh..."

But the next second-

Xu Heng said calmly, "At least you have to go through the process in your mind before you can give an answer."

Pfft! ! !

What the hell! ! !

Xu Heng, the usual exam questions are so simple, you can just do the math!

You don't need to play straw paper!

How to do this kind of Mathematical Olympiad competition questions, are you still like this?

Yang Kaixuan no longer knew what to say.

His mind was blank and he was at a loss for words!

Geek!

Suddenly, he realized that Xu Heng said that the Mathematical Olympiad competition is simple, not just talking about it.

People have real talents and real learning!

Yang Kaixuan, "I'm still too young! Or I underestimated you too much!"

"Hiss...Xu Heng...you...!!!"

Xu Heng interrupted Yang Kaixuan's shock, "With this time, you should read a few more questions."

Xu Heng continued to brush his TV.

Yang Kaixuan opened and closed his mouth, his whole body was like an eggplant beaten by frost.

It's not that I don't know if I'm at the same table with Xu Heng. Only when I'm at the same table do I know what the real nightmare begins.

The harder I work, the more I and Xu Heng's perception becomes greater!

The harder you work, the more you can get in touch with new knowledge, Yang Kaixuan feels that he is doing it again!

But as soon as he turned his head, Xu Heng, who was playing, took care of the new thing he had just learned.

Yang Kaixuan was depressed.

Did he learn new skills, or did Xu Heng unlock new abilities?

I finally stayed up until late for self-study and school.

Yang Kaixuan, who returned to the dormitory, was still working hard on the questions.

The other roommates came over and walked away frowning without staying for a minute.

"Hiss! This question..."

"Farewell..."

"Yang Kaixuan, you are the only one who can do it... um... only you and Xu Heng can do this kind of problem! It gives me a headache just looking at it!"

I wanted to talk about Yang Kaixuan, but I saw Xu Heng again.

He immediately changed his tune.

Xu Heng washed up, went to bed, and continued to play with his mobile phone.

Tang Kaixuan sighed, and retorted, "I am me, Xu Heng is Xu Heng! I can't do it! Your words can only be used on Xu Heng!"

"Do you think Xu Heng said that these questions are too simple, that he was joking and pretending to be thirteen?"

Several people in the dormitory looked at each other.

"Yang Kaixuan, you are too modest!"

Yang Kaixuan was stunned, with an inconceivable expression on his face, "You guys think I'm humble? What I'm telling is the truth! I really don't know how to do these questions! I still want to ask Xu Heng for advice!"

With that said, Yang Kaixuan stood up.

"If we say that the college entrance examination questions are designed to allow most candidates to get points, but not high scores! Then the Olympiad questions are designed to make most candidates unable to understand, and only a very small part of them can understand. Yes, there are very few of them!"

Everyone was skeptical, "It's not that exaggerated?!"

Yang Kaixuan ignored these people, and stood beside Xu Heng's bed in front of them, "Xu Heng, I have a question for you, do you have time?"

Xu Heng turned his head and put down the earphones.

topic:

设P为椭圆（x2/25）+（y2/16）=1长轴上一个懂点，过点P斜率为k直线交椭圆于两点。

If the value of 丨PA丨2+丨PB丨2 only depends on k and has nothing to do with P, find the value of k.

Xu Heng stood up, "Paper and pen."

Yang Kaixuan sent it over immediately.

Xu Heng wrote while talking.

The calculation process seems to be a few simple steps, but the values ​​involved in it are too large, and all kinds of a2k2 are both numerators and denominators.

"."According to the above, we can get..."

丨PA丨2+丨PB丨2=（x1-a）2+y12+（x2-a）2+y22

“然后解开，令 -800k2=0，次哦那个人得出k=±4/5。”

In Xu Heng's mouth, what he said was called lightness.

But when everyone watched this step, they were dumbfounded!

Just the fraction multiplied by (k2+1) gave them a headache.

分子：（ -800k2）a2+800（16+25k2）

Denominator: (16+25k2) 2

When Xu Heng listed these, the calculator was useless, so he drew on the straw paper and gave the answer!