There were not many words on the blackboard. Wu Tong put his schoolbag down casually and read the words while walking up to the stage.
n is a positive integer, S={x, y, z·····, try to find the minimum number of planes whose union contains S but does not include (0, 0, 0).
As soon as she read the question in the first grade, Wu Tong clearly felt the difficulty of this question. It was quite high. It was comparable to the classic sixth question of the 1988 IMO exam that she had done.
Instantly entering a deep learning state, Wu Tong quickly deduced and extracted the key points in her mind, and a storm of thoughts unfolded in the invisible depths of her mind. In an instant, inspiration illuminated her thinking and she could introduce the Lagrange mean value theorem. She picked up the chalk and began to write on the blank space on the blackboard.
Solution: Let the degree of the polynomial p(x) be N, and define the difference operator △ to satisfy...
Let I be the constant operator. According to Lagrange's mean value theorem, we know that:
△p(x)=p(x+1)-p(x)···
·····
Take x=y=z=0, and we get f(0, 0, 0) = `····
This contradicts f(0, 0, 0) ≠ 0, so m ≥ 3n, and the equality is established as shown in the previous example...
After fluently writing down the proof process that took up nearly an entire blackboard, Wu Tong softly explained, "This is a relatively simple and straightforward solution. There's a more complex solution that won't fit on the blackboard, so I won't go into details here!"
Hehehe···Hehe···
The other provincial team members in the audience felt like they were hit hard twice in an instant. "God" on the stage, please consider the heartache of the people below the stage. Is this the difference between them and the first place with full marks?
They have been thinking hard and still haven't found a way out, while the person on the stage casually read the question and wrote down the proof on the blackboard. They looked very struggling and hadn't fully understood it yet, but she told them that she had another solution, but she didn't write it down because it couldn't fit on the blackboard?
Is this not allowing people to survive?
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