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

topic:

Known positive numbers a, b, c satisfy: 5c-3a≤b≤4c-a, clnb≥a+clnc, what is the value range of b/a?

That's it?

After reading the title, Xu Heng said directly, "[e, 7]."

Not even the feasible domain, etc. These things are not mentioned.

After reading the question, Xu Heng directly raised his head, frowned, and a helpless expression showed everything.

The math teachers took a deep breath, "Hey... hiss... Xu Heng! Are you serious? What do you mean, this question is too easy?"

"???"

"Teacher Ge, let me just say it! The question you asked is not difficult enough!"

Teacher Ge?

Xu Heng frowned.

Immediately, a teacher came over, "Student Xu Heng, this Teacher Ge is a big devil invited from other provinces by our new education director!"

"The candidates in his hands are horrible every year!"

"The difficulty of his examination paper can be said to be the most difficult in the whole country!"

Xu Heng narrowed his eyes slightly, "I've heard it before!"

And that Teacher Ge was also very interested after seeing Xu Heng.

"Student Xu Heng, hello, I've heard about it for a long time!"

Xu Heng smiled and shook hands with Teacher Ge, "Mr. Ge, you are the one who is famous!"

After the two exchanged pleasantries, Teacher Ge said with a smile, "Student Xu Heng, since my question is simple, it can be regarded as an appetizer, why don't you look at this question again?"

"Do you have any good suggestions?"

There is no style of Mathematical Olympiad competition at all!

It is really the type of questions that only college entrance examination mathematics should have!

topic:

It is known that two sequences {an} and {bn} whose items are all positive numbers satisfy a(n+1)=(an+bn)/under the root sign (an2+bn2), n∈N*,

(1) Let b(n+1)=1+bn/an, n∈N*, prove that the sequence {(bn/an)2} is an arithmetic sequence;

(2) Let b(n+1)=(square root 2)*(bn/an), n∈N*, and {an} is a geometric sequence, find the values ​​of a1 and b2.

Just such a question!

The shot is to cry high school candidates!

Teacher Ge's question was approved by all the teachers in the math group.

Xu Heng looked at it and also gave a thumbs up.

"Teacher Ge, you're amazing!"

Teacher Ge has long heard about Xu Heng's strengths, and most of the reasons for being invited here to present papers this time are because of Xu Heng.

He wants to meet Xu Heng!

He wanted to meet this legendary super academic!

At the same time, he also wanted to prove Xu Heng's strength!

After all, seeing is believing!

The previous question was indeed an appetizer for Mr. Ge.

But for other teachers, apart from Xu Heng, that question is still very difficult!

But if it was done for Xu Heng, they wouldn't be surprised even if Xu Heng could give the answer in seconds!

Teacher Ge, too!

If Xu Heng has to think about that question for a long time, then he has misjudged the person.

But for this question, Mr. Ge gave Xu Heng less than an hour!

After all, the difficulty of this question is at the nightmare level.

Even he himself felt, "This is the best time I have performed in so many years! It is also... the most difficult time to solve the problem!"

The teacher who gave the paper...performed the best...naturally it means that the questions are the most difficult and tricky!

Teachers, "!!!"

They all gasped.

It's hard for Mr. Ge to get out the paper!

Not only the mathematics group, but other groups have also heard about it!

Other teachers also complained.

"High school dismissed!"

"College entrance exam phobia!"

"The mentality is broken! The college entrance examination is crying!"

"Wait, these seem to have all been produced under the shadow of Teacher Ge's writing..."

"..."

It can be seen!

Even on the Internet, Mr. Ge became popular because of the difficulty in posing the questions.

At this moment, Xu Heng raised his eyebrows slightly in the face of Teacher Ge's difficult problem.

All the teachers in the math group also fell silent.

But only 2 minutes later, Xu Heng stepped onto the blackboard and wrote:

Solution: (1) because b(n+1)=1+bn/an

所以a（n+1）=（an+bn）/根号下（an2+bn2）=b（n+1）/根号下（1+（bn/an）2）

So b(n+1)/a(n+1)=square root(1+(bn/an)2)

所以（b（n+1）/a（n+1））2-（bn/an）2=（根号下（1+（bn/an）2））2-（bn/an）2=1（n∈N*）

So {(bn/an)2} is an arithmetic sequence with 1-digit tolerance.

The first question is easy to get!

It took Xu Heng less than 4 minutes from thinking to writing!

Teacher Ge has been silent!

But the scalps of the other math teachers around were numb.

"This is a topic that Teacher Ge has prepared for a long time!"

"It took me a long time to make it!"

"Hiss... this, this, this... Although I have already prepared myself, I know Xu Heng's excellence, but... hiss... I am still quite shocked."

Teachers, "!!!"

But Xu Heng didn't intend to stop. After finishing the first question, he wrote (2) on the blackboard.

It was only then that everyone came to their senses. In those 2 minutes just now... they didn't just think about the first question, but both questions together!

All the teachers looked at Teacher Ge.

But Teacher Ge is still very calm.

"Until the last word of the result is written, I will not give affirmation."

This is Teacher Ge's attitude!

Xu Heng continued:

因为an＞0，bn＞0，所以（an+bn）2/2≤an2+bn2＜（an+bn）2

所以1＜a（n+1）=an+bn/根号下（an2+bn2）≤根号2

Assume that the ratio of the geometric sequence {an} is q, and q>0 is known from an>0, and the following proves that q=1 by counter-evidence

若q＞1，则a1=a2/q＜a2＜根号2，所以当……

contradiction!

If 0<q<1, then...

……

所以bn=[根号2±（根号2）2*根号下（2-（根号2）2）]/（根号2）2-1，最终结果等于根号2

So a1=b2=square root 2

Xu Heng put down the chalk, and Teacher Ge was the first teacher to applaud.

He has suppressed his shock for a long, long time!

Seeing Xu Heng's speed and accuracy in answering questions with his own eyes today, he was overwhelmed with admiration.

"I'm convinced! I'm really convinced!"

Looking at Xu Heng, Teacher Ge's eyes were full of awe!

Xu Heng smiled, "Teachers, it's gone! Is there no topic?"

"I'm here to say something!"

"Don't try to embarrass me! I'm on the same front with you! We're giving the questions to the students in the third year of high school!"

"You test me as a sophomore in high school, what kind of skills are you?! Do you think so?"

"Everyone, don't you think so?"

All the teachers laughed loudly, "Student Xu Heng was impatient in the exam!"

Xu Heng rolled his eyes, "That's not what you said! You tried every means to test me, but there was no result. Why bother?"

There is no result here, it is Xu Heng who knows it, there is no need for this!

He is in such a big meeting room, bluntly!

Xu Heng's words were powerful and clear!

Let all the teachers gasp.

Yes!

There is no result at all!

So don't make these useless attempts, let's work out the questions together with peace of mind!

"I am not your enemy!"

After Xu Heng finished speaking, he even sighed. Teacher Ge stepped forward and invited Xu Heng.

"Student Xu Heng, I have a problem here. Come and take a look, student Xu Heng? Let's improve it together?"

Teacher Ge plus Xu Heng!

Strong alliance!

Just as they stood together, the teachers in the math group held their breath.

Nima!

Strong in the strong!

This involuntarily reminded them of an advertisement for a certain battery!

One quarter is better than six!

What's even scarier now is that there are two stronger than six knots!

These two are united!