“逼近”是高等数学尤其是函数论中思考问题的一种重要思想方法。将它用于解决某些非常规的初等数学问题,有时显得十分凑效和巧妙。 例1 求一个四位数abcd,它是11的倍数,且b+c=a,同时bc是完全平方数。 分析:(1)四位数共有9000个,对这9000个一一进行试验,看哪几个同时符合这三个条件,即可找出所有的解。可见,本题是显然可以解决的,只是试9000次太慢了! “Approximation” is an important way of thinking in thinking in higher mathematics, especially in function theory. Using it to solve some of the unconventional elementary math problems is sometimes very fruitful and clever. Example 1 Find a four-digit abcd, which is a multiple of 11, and b + c = a, while bc is a complete square. Analysis: (1) There are a total of 9,000 four-digit numbers. Test the 9000 one by one. See which of these three conditions meet the three conditions at the same time and find out all the solutions. Obviously, this question can obviously be solved, but it is too slow to try 9000 times!