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

Xu Heng had a headache, "They can only blame themselves! They insisted on pretending to be so bitter and vengeful to come up with this question, since they were all prepared..."

Geek!

Suddenly, Sun Jianhua was stunned, "Wait! Student Xu Heng, you seem to have misunderstood it!"

And at this time, the only remaining math teacher among the nine people put down his pen and let out a long sigh of relief.

He looked at Xu Heng, gritted his teeth, "Student Xu Heng, please enlighten me!"

PS: Thank you [Good Big Nine] [Round Balls] for their support!Kneel for all support! .

Chapter 283

Sun Jianhua looked at Xu Heng, he suddenly thought:

Now that Xu Heng has seen through all of this, he must also think that these people and these questions are all prepared in advance!

Xu Heng shrugged his shoulders and said with a smile, "Besides, I have prepared in advance, so why can't I prepare some difficult questions?"

"It is said that those questions are very easy to me, but give me more difficult ones!"

"But actually, isn't it still unsatisfactory?"

"I looked at it, and the feeling of answering the questions is gone!"

"Hey……"

"Mr. Sun, just tell the truth, you must be very disappointed, aren't you?"

Sun Jianhua, "*%#￥#@￥%..."

"Wait a minute! Student Xu Heng, you seem to have misunderstood something."

Xu Heng, "???"

"Yes! We were invited by the director, and he also chatted with us about the process, but..."

Xu Heng, "But? Elder Sun, it's okay if you say it, don't hesitate."

Sun Jianhua took a deep breath, "But this link really didn't exist before!"

"It should be the director's impromptu idea!"

Xu Heng, "???"

The next second, Xu Heng looked at the director, and then at all the teachers present, all of them had complicated eyes.

But when they looked at the director, their resentment became more obvious.

Xu Heng, "!!!"

"So... these teachers are really... really giving me questions?"

Sun Jianhua nodded seriously, "I think it's true!"

Xu Heng felt overwhelmed by the heights, and sighed, "Hey...to be honest, I almost wanted to say just now: Teachers, especially those who are still working on the questions, I beg you, Make it a little more difficult!"

Sun Jianhua, "%￥@@￥￥%*..."

He's all bad.

"Student Xu Heng, your height is already far higher than what they have come into contact with!"

"They pose questions, to you, it's like a mantis shaking a cart or a mayf shaking a tree!"

"Just play around with it!"

Xu Heng frowned slightly, "That's the only way to go."

Back to the long table.

The math teacher's question had already been handed to Xu Heng.

topic:

已知函数f（x）18=[1/根号下（1+x）]+[1/根号下（1+a）]+[根号下（ax/（ax+8））]，x∈（0，+∞）。

(1) When a=8, find the monotone interval of f(x);

(2) For any positive number a, prove: 1<f(x)<2.

This is the last hope!

This is the last hope of the nine representative teachers!

This is the last stubbornness of more than 100 teachers present!

They all pinned their hopes on the math teacher.

They raised their heads and looked at the subject.

Even the teachers and even the team leader in the math group couldn't help giving a thumbs up.

"Okay! It's really amazing to be able to come up with such a topic in such a short period of time!"

"This question can be used as the final question in the college entrance examination!"

"Student Xu Heng, this may be unfair to you, but..."

Before he finished speaking, Xu Heng took a pen and wrote down:

f(x) increases monotonically on (0,1] and decreases monotonically on [1, +∞).

Then he raised his head, "The first question is so simple, so you don't need to write the process, right? It's nothing more than asking for a guide."

As soon as the words came out, everyone said, "!!!"

Even Hong Jingjun's eyes lit up.

"Absolutely! This little guy is absolutely abysmal! Old Sun, did you see that! Did you see that!"

"His talent in mathematics far exceeds my imagination, and it also far exceeds his level in other areas!"

"Oh my god! What about oral calculations! This is?!"

"Let's just deduct it!"

"How can you tell the answer in such a short period of time!"

"hiss……!"

Hong Jingjun expressed the shock of all the teachers!

They looked at Xu Heng's calm expression, and then at the math teacher's eyes waiting...

Obviously, what Xu Heng wrote down is the correct answer!

The math teacher, "!!!"

He looked at Xu Heng like a freak.

Xu Heng, "Hey! Teacher! Did I answer the second question directly?"

"Teacher? Teacher!!"

The math teacher just came back to his senses and nodded in shock.

Xu Heng then bowed his head and began to write down the answer to the second question.

For any given a>0, x>0,

因f（x）=[1/根号下（1+x）]+[1/根号下（1+a）]+[根号下（1+8/（ax）]，

If let b=8/ax, then abx=8...①,

f（x）=[1/根号下（1+x）]+[1/根号下（1+a）]+[根号下（1+b）]……②

Proband score (x) > 1.

because……

……

由由2+a+b+x≥2根号下（2a）+2根号下（bx）≥……=8，

Get a+b+x≥6.

So f(x) =...

……

Just the calculation of this step alone made all the teachers' scalps tingle!

It's not the students who get numb, but the teachers!

Even they find it too difficult!

But in Xu Heng's writing, everything is so easy.

Just one of the fractions has dissuaded many people.

Molecule: 1+(a+b+x)+(ab+ax+bx)+abx

Denominator: (1+x) (1+a) (1+b)

Who can bear this!

Who can bear this!

After that, it is also necessary to prove that f(x)<2

From the symmetry of x, a, b in formula ①②, we might as well set x≥a≥b, then 0<b≤2.

When a+b≥7, then a≥5, so x≥a≥5,

because……

……

That is, ab+8>(1+a)(1+b),

That is, a+b<7, according to ③, this is obvious.

Therefore, ⑦ is proved, so f(x)<2 is obtained from ⑥.

To sum up, for any positive number a, x, there is 1<f(x)<2.

Eloquently, Xu Heng got all the answers within 3 minutes.

Teachers, "!!!"

Especially those teachers in the math group, their scalps were numb.

"This, this, this..."

"How is this possible! Student Xu Heng, you..."

The math teacher who came up with the question stared at Xu Heng's problem-solving process.

"It's right! His process is right! His thinking is right! Absolutely right!"

"!!!"

The math teacher stood up suddenly, stared at Xu Heng, and then bowed deeply.

Ninety degrees!

After bending down, his neck turned red, and he said in a deep voice, "I'm sorry, student Xu Heng!"

"Although we had a purpose to speak ill of you before! But... I still have to apologize!"

"After all, I said you were bad, so please accept my apology!"

"In addition, the bigger aspect is that I was conquered by you!"

"I am overwhelmed by your talent!"

"You are from our province... No! You are a rare talent in our entire country!"

"To be honest, we all knew how powerful you are from the beginning, but we all want to see with our own eyes how powerful you are!"

"Now that we have seen it with our own eyes, we are convinced!"

Said a lot in one breath!