There is a cuboid, the product of the front and the upper two areas is 209 square centimeters, and the length, width and height are prime numbers. Find its volume.
I saw it and thought: this question is really difficult! Only knowing the product of two surface areas, the volume must also know the length, width and height, but there is no hint at all. How does this start?
Just as I was scratching my head, a colleague of my mother came. He taught me to use the idea of equation to solve it first, but I am not very familiar with this method of equation. So, he taught me another way: list the numbers first, and then exclude them one by one. First, we listed a lot of numbers according to the requirements of the topic, such as: 3, 5, 7, 1 1, and then we began to exclude them, and then we found that only1and 19 were left. At this time, I thought: one of these two numbers is the length of the common side of the front of the cuboid in the question; One is the front of the cuboid, and the other is the division of the previous one.
Sum of side lengths (all lengths are prime numbers). So, I began to tell which number these two numbers were.
The final result is 374 cubic centimeters. My formula is: 209 =119 = 2+171× 2×17 = 374 (cubic centimeter).
Later, I checked this problem with what I learned this semester: prime factor decomposition, and the results are exactly the same.
I am happier than anyone to solve this problem. I also understand the truth that mathematics is full of mysteries, waiting for us to explore.
I met another math problem today, and it took me a lot of effort to solve it. The topic is: there are 30 birds in two trees, and 4 birds fly away from the second tree first. At this time, tree A flew to tree B with three birds, and the birds on the two trees were just equal. How many birds are there in each tree?
As soon as I saw the topic, I knew it was a reduction problem, so I solved it by the method of reduction problem. But when I checked, I found something was wrong. I will do it again more seriously. I think there are as many as four missing, half of them are 13, and the restored B-tree is14; A tree is 16. The formula is: (30-4) ÷ 2 = 13 (only); 13-3+4 =14 (only); 30- 14 = 16 (only). The answers are: a tree 16 and b tree 14.
By solving this problem, I understand that no matter what I do, I should be careful, otherwise, even if I master the solution to the problem, the result will be wrong.