From child prodigy to chief scientist

However, this vocabulary task did not specifically mark "valid". As long as the study time is continuous, it should be fully counted.

Of course, if the system didn't start collecting statistics from noon today, then things would be completely different.

The next day, Xu Xiao didn't dare to let her guard down. She fought off her sleepiness and got up early. After breakfast, she went to the classroom to study.

To Xu Xiao's delight, the progress of the entry task jumped to 2/30 days at around 7 p.m. that day.

This proves that Xu Xiao's previous guess was indeed correct. According to such statistical rules, even if the daily study time requirement for this task is increased by two or three hours, it is still entirely achievable.

Even if Xu Xiao didn't go to the extreme of studying with a book while eating, completing this task at a normal pace wouldn't be difficult.

However, to be on the safe side, Xu Xiao still hopes to complete the daily study time targets as early as possible to avoid interrupting the task progress due to unforeseen circumstances.

That morning, Xu Xiao came to audit a class in Class 1 of Senior Three as usual.

After these days of accumulation, Xu Xiao's academic level in all subjects has improved significantly.

In particular, the subject of mathematics has exceeded 100 points.

Mathematics was already Xu Xiao's strong suit, and the recent intensive training for math competitions has further enhanced his mathematical abilities.

According to the system's assessment, Xu Xiao's mathematics skills have now fully met the requirements for the college entrance examination.

It's important to know that the system's assessment of academic level is extremely rigorous.

Such an evaluation indicates that Xu Xiao has a chance to achieve a perfect score in the college entrance examination mathematics.

After class, Xu Xiao went to the restroom. When she came back and was about to sit back down, she saw two students next to her seemingly discussing something.

"This problem is really a bit strange. After I homogenized it and expanded it, I got more and more confused as I calculated it.

"Based on the conditions, if we replace the 3 on the right with a+b+c, the entire inequality becomes a homogeneous quartic inequality."

"The resulting formula is somewhat similar to Schul's inequality, except for the degree. I tried to factor it, but I just couldn't figure it out..."

The speaker, Zheng Qinhong, achieved the highest score in the science stream of the grade in the last monthly exam, with a score of 698, and even got a perfect score of 150 in mathematics.

He saw this question in a workbook, and it stumped him for quite a while, but it only fueled his fighting spirit.

"I just tried using Lagrange, and it should be able to prove it, but the steps to prove the equality condition are too complicated, and this method is beyond the scope of the subject."

Another student, Qin Wei, also ranked in the top five in the grade in the last monthly exam, and only lost one point in math.

Xu Xiao wasn't one to join in the fun, but seeing that these two top students were stumped, she still curiously went over to look at the questions.

【已知 a，b，c >0， a+b+c=3，求证：(a^2+b^2+c^2)^2≤ 3(a^3+b^3+c^3)+ 6abc。】

"This problem can be solved by first transforming it using Schul's inequality, and then discussing it by case..." Xu Xiao thought to herself.

Recently, Xu Xiao has been exposed to many math competition problem-solving methods, which has broadened his thinking considerably.

This method involves knowledge that is definitely beyond the scope of normal high school mathematics. Even if you can solve it, you will still need to prove those out-of-syllabus concepts again, otherwise you still won't get the points.

Since this is a problem from a high school math workbook, there must be a better way to solve it.

Seeing Xu Xiao approach, Zheng Qinhong joked:

"Oh, the child prodigy is here."

Because of Xu Xiao's exceptional intelligence at a young age, many people in his class liked to call him a child prodigy.

Xu Xiao naturally didn't consider himself a child prodigy, but since everyone was willing to call him that, he didn't mind.

"Hey, perfect timing! Come help us with this problem. Do you think you can come up with a good solution?"

Qin Wei appeared to be joking, but deep down she still had high hopes for Xu Xiao.

Being able to score 140+ in high school math at this age is enough to prove just how strong Xu Xiao's math skills are.

In particular, Xu Xiao also secured a spot in this year's Yucai High School Mathematics Competition, defeating many students who had been preparing for the competition for a long time, which is a remarkable achievement.

"Okay, let me go back and think about it some more..."

Xu Xiao didn't bother to copy down the questions; she simply sat back down in her seat.

With my strong memory, I can easily remember these kinds of questions at a glance; the key is to find a clever method.

Once in a focused state, Xu Xiao quickly searched his mind for any knowledge that might be useful.

Initially, Xu Xiao's approach was to utilize Cauchy's equation of the difference of squares.

However, this is still a competitive knowledge, and although it is simpler than the method of Schul's inequality, it is still not a particularly preferred method.

"Wait a minute... it seems like it can also be done using direct algebraic expansion."

With this new idea in mind, Xu Xiao immediately began to deduce its meaning.

The initial steps are not particularly special; we first use the condition a+b+c=3 to perform substitution, and then expand and simplify.

However, Xu Xiao's handling of the factorization step was very elegant.

Not only did it not use any knowledge beyond the requirements of high school mathematics, but it also cleverly grouped and transformed the expressions.

Finally, we just need to check the non-negativity of this expression.

Having successfully completed the proof, Xu Xiao felt a faint sense of joy.

Being able to solve a problem that even Zheng Qinhong and Qin Wei couldn't solve immediately is something Xu Xiao should be proud of.

The school bell hadn't rung yet when Xu Xiao took her notebook and went over.

"I've finished verifying it. You two can take a look."

"So fast? Let me see!"

Zheng Qinhong took the notebook from Xu Xiao's hand and quickly began to read it.

He had initially thought that Xu Xiao might use some competition techniques to solve this problem.

But after he finished reading Xu Xiao's proof process, he realized that things were not as he thought.

"Holy crap... I can't believe they can group people like this! How come I never thought of that?"

To be honest, Xu Xiao's approach wasn't particularly outlandish, but if you hadn't seen this line of thinking, it would have been really hard to come up with the same method.

After seeing Xu Xiao's proof, Qin Wei also looked enlightened.

"I told you Xu Xiao might be able to do it. See? Zheng Qinhong, are you convinced now?"

"Why should I be dissatisfied? Maybe in a few months, the prodigy's score will surpass ours."

"It seems I'll have to ask Xu Xiao for help more often when I encounter problems I don't know how to solve."