Chapter 224 (1/2)
Dong Dong!
Cheng Nuo knocked on the blackboard heavily and looked at the people in the mathematics department under the platform with a smile, ”we continue to talk.”
”If both a and A-1 are unit roots, let B be a complex conjugate of a, with ab = | a | 2 = 1, (A-1) (B-1) = | A-1 | = 1.”
”A = (1 ± √ 3I) 2 can be obtained, α = (1 + √ 3I) 2, β = (1 - √ 3I) 2.”
”If A-1 = 0, then a = 1.”
”So the roots of F (x) can only be 0, 1, α, β, and the roots of F (x + 1) can only be - 1, 0, α - 1, β - 1...”
The formulas are written on the blackboard by Cheng Nuo.
Shua Shua Shua!
Line after line of closely related mathematical formulas, for the students of Tsinghua mathematics department, although not a heavenly book. But it takes time to understand.
But Cheng Nuo did not give people time to understand.
In people's eyes, Cheng Nuo is like writing the calculation steps in his mind.
Without any pause, without any hesitation, Cheng Nuo wrote on the blackboard with a Shua Shua, while his mouth was like a barrage of explanation.
It is not like a freshman at all. It is more like an old teacher immersed in education for many years.
Soon, the whole four blackboards were filled with two by Cheng Nuo.
However, the problem is still unsolved.
”Let f (x) = C · x ^ m · (x-1) ^ n, with F (x ^) = C · (x ^) ^ m · (x-1) ^ n = C · x ^ (2m) · (x-1) ^ n · (x + 1) ^ n, f (x + 1) = C · (x + 1) ^ m · x ^ n.”
”Substituting into the equation, C · x ^ (2m) · (x-1) ^ n · (x + 1) ^ n = C · x ^ (M + n) · (x-1) ^ n · (x + 1) ^ M. If C ≠ 0, the equality holds if and only if M = n, C = 1. So f (x) = x ^ m · (x-1) ^ M
Finally, Cheng wrote the results on the blackboard.
”Therefore, only 0, 1 and x ^ m · (x-1) ^ m!” are the polynomials satisfying the conditions
We're done. We're done!
After finishing the last stroke, Cheng Nuo confidently smiles, leaving only the chalk on the desk.
The audience is silent!
Pa Pa Pa ~ ~!
Standing on the side of the platform, Liao Zhixing looks at Cheng Nuo with satisfied and appreciative eyes and claps gently.
Pa Pa Pa ~ ~!
The mathematics students in the class clapped at the sight of Liao Zhixing, and they all clapped with their hands. Except for one, of course.
The applause went on for a long time before it stopped.
”Teacher, this is my own problem-solving steps, do not know whether it is correct, but also ask the teacher for advice.” Cheng Nuo's tone is very sincere.
Liao Zhixing said with a smile, ”right! absolutely right! This is a perfect solution to the problem! I can't find any mistakes
”Come on, let's clap for this classmate's performance again!”
If the teacher says something, you can't follow it!
As a result, the classroom broke out clapping again.
Cheng Nuo stood on the platform, a helpless, flattered look, he repeatedly waved his hands, ”no, no, stop. You don't have to stop... ”
Cheng Nuo is positive facial expression, ”I this just solved a problem that can't be simpler any more, it's not to be proud of.”
”I believe that the students here must have worked out this problem earlier than me, but I'm sorry to raise my hand.”
Cheng Nuo said painstakingly, ”however, I still hope that all of you here can be more positive. Don't fiddle, like a flower girl. Since you have come to Tsinghua, you should not be lazy! Studying hard is the right way! If we don't even have the courage to speak on stage, how can we become a useful pillar of society? ”