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

Just as I was about to wash up, a roommate came back with a dejected face.

Yang Kaixuan and others surrounded him, "How's it going? I asked you to go to the playground for a self-study at night. How's it going?"

"???"

"Stop pretending! Come on! Tell me!"

"Haven't you admired her senior sister for a long time?"

"He took the initiative to ask you out this time, it must be a success!"

But the classmate sighed, "It's hard to say."

This classmate's name is Zhao Dongyu, 1.8 meters tall, and he is a bit handsome, but compared with Xu Heng, he is much worse.

Zhao Dongyu looked at everyone, and finally targeted Xu Heng.

Xu Heng, "???"

"Zhao Dongyu, why are you looking at me?"

Zhao Dongyue pouted, "I don't want to see you either! But I can't do without you!"

Xu Heng, "???"

Yang Kaixuan and the others said, "???"

"What's the matter?"

Zhao Dongyu sighed, "Hey! Let me tell you this! Hey... Senior sister asked me out to give me a question. I hope Xu Heng can help me solve it."

Yang Kaixuan and the others gasped immediately, their faces twisted, "Can it still be like this?"

"I'll go and go...%￥#@#￥￥%..."

Zhao Dongyu was extremely helpless.

"Headache! I have a headache!"

"What's more terrible is this question, I don't know how to do it yet!"

"Are you angry?"

Everyone nodded.

Zhao Dongyu, "Huh...so, Xu Heng, I can only trouble you!"

Xu Heng, "Eh... can I refuse?"

Zhao Dongyu curled his lips, "Be yourself! You have a lot of adults, please help me! I asked you! I beg you!"

Xu Heng seemed to have seen a lifelike... a dog.

Zhao Dongyu, "Xu Heng! Do me a favor!"

"I gave them a guaranteed ticket!"

Xu Heng rolled his eyes, "Is it your girlfriend? Does it count? Doesn't it count, why should I help?"

"First, I don't know her!"

"Second, I don't help other people except those I know. Have you ever seen me help other people?"

Yang Kaixuan and the others shook their heads.

"It seems to be true!"

Zhao Dongyu was stunned, "I... Nima... I... this, this, this..."

"If you help me solve this problem, don't I have the capital to chase people! You come and go! You are a matchmaker anyway!"

"Really? Xu Heng, do you think so!"

Everyone also began to encourage!

"Hey! This is a good idea!"

Xu Heng, "???"

"What's the matter, you guys are too insane!"

Xu Heng couldn't help complaining, "Is this the love world of Xueba?"

Everyone complained collectively, "You are the top student, okay?"

Xu Heng, "...%￥##@##￥#..."

Xu Heng nodded under Zhao Dongyu's hard work, "You show them a few first, what if they know it! I don't need me anymore!"

"I'm going to wash up first."

Zhao Dongyu's eyes turned to Yang Kaixuan.

Yang Kaixuan accepted the order in the face of danger, frowned, and said righteously, "Okay! Come on! Show me!"

topic:

It is known that a>0, the function f(x)=ax-bx2

(1) When b>1, if for any x∈R, f(x)≤1, prove that a≤2 under the root of b;

（2）当b＞1市，证明：对任意x∈[0,1]，|f（x）|≤1的虫咬条件是b-1≤a≤2根号下2；

（3）当0≤b≤1时，讨论：对任意x∈[0,1]，|f（x）|≤1的充要条件。

Yang Kaixuan looked at the question, his expression froze on the spot, "The college entrance examination question...?"

Zhao Dongyu frowned, "It's not a college entrance examination question, what kind of question is that? Isn't it normal for her to be a college entrance examination question in her third year of high school?"

puff...

Yang Kaixuan couldn't help but twitched his eyes, "But I... a sophomore in high school..."

Zhao Dongyu, "Ah..."

Everyone was also stunned.

Only then did they realize that they had already compared Xu Heng to Xueba.

Xu Heng is a top student, and as a top student, what questions can't he?

Sure will!

What's wrong with Super Gang?

still will...

But they overestimated Yang Kaixuan.

When Yang Kaixuan said these words, they realized that not everyone can be Xu Heng.

"."Fine……"

Zhao Dongyu took a deep breath and waited for Xu Heng.

When Xu Heng came back, everyone stared at him.

Xu Heng, "???"

"You helped him solve it?"

Everyone shook their heads!

Yang Kaixuan curled his lips, "You are too overestimating us! You should do it!"

Zhao Dongyu handed the question to Xu Heng.

Xu Heng looked at it, and couldn't help but frown.

"Forehead……"

Zhao Dongyu said bluntly, "It's more difficult! I don't know what stimulated these teachers, and they started to find various problems, especially the final final questions of the college entrance examination!"

"One is more difficult than the other! One is more difficult than the other."

"Senior sister's grades were good, but now she has been hit hard."

Hearing these words, Yang Kaixuan suddenly had an idea in his mind, he suddenly looked at Xu Heng, "Xu Heng, it's not because you stimulated the math teachers in our school before, that's why you gave them such a difficult job. It's about the topic, right?"

Xu Heng, "???"

Don't say it!

It's possible!

Yang Kaixuan, "Xu Heng, I'm afraid you have irritated all the math teachers in our school!"

"Because you and Yue Pingting are both sophomores in high school! Even Yue Pingting knows everything you asked for, especially the college entrance examination questions, so they are all in a hurry!"

"The sophomores can get the college entrance examination questions at their fingertips, and their seniors are really like ants on a hot pot."

Xu Heng, "%￥#@##@￥￥......"

After waving his hand, Xu Heng said, "Lecture topic! Don't make these useless things."

"quickly come."

Zhao Dongyu was the most serious. He brought two copies of paper and pen and gave one to Xu Heng.

Xu Heng started speaking directly.

"Since f(x) ≤ 1 for any x ∈ R, then..."

Write on paper:

So bx2-ax+1≥0 is always established,

So △=a2-4b≤0,

So a≤2 root sign under b.

Xu Heng, "Let's look at the second question next."

Proof: Necessity:

For any x∈[0,1], |f(x)|≤1, that is, -1 and f(x), it can be seen that -1≤f(1), that is, ab≥(get Good 1

So a≥b-1

For any x∈...

……

因为b＞1，a≤2根号下2，对任意x∈[0,1]可以推出ax-bx2≤2（根号下b）x-bx2≤1

That is, ax-bx2≤1

So -1 ≤ f(x) ≤ 1

In summary, when b>1, for any x∈[0,1], the necessary and sufficient condition for |f(x)|≤1 is that b-1≤a≤2 under the square root of b

Xu Heng looked at these people, "Do you understand? Do you understand? If you understand, let's look at the third question..."

Yang Kaixuan was the first to interrupt Xu Heng, "Wait, wait a minute! I'll take care of it..."

He raised his head and looked at everyone, "You all understand? Don't feel ashamed! In front of Xu Heng, why do you feel ashamed!"

"No, it won't!"

"I don't understand, I just don't understand!"

Zhao Dongyu also breathed a sigh of relief at this time, and looked at Xu Heng helplessly, "Xu Heng, give us a little more time, I will digest it, and then I will ask you the third question."

Xu Heng, "Okay! I'll go to bed first."

Xu Heng went up with a pen and paper, and after going to bed, he began to answer the third question.

Solution: Because a>0,0<b≤1, for any x∈[0,1]...

……

所以当a＞0,0＜b≤1时，对任意x∈[0,1]，|f（x）|≤1的充要条件是a≤b+1.

After Xu Heng finished writing, ten or twenty minutes passed.

The roommates looked at Xu Heng and asked Xu Heng for confirmation.

Xu Heng gave them the answer and said it verbally, so they understood.