引言
数学难题一直是考验学生和学者智慧的重要方式。在数学的学习和研究中，一些经典的难题常常成为焦点。本文将详细介绍16大数学难题的破解模型及答案详解，帮助读者深入理解这些难题的解题思路。
1. 循环小数化分数
解题模型
设元—扩大——相减（无限变有限）相消法。
例子
将0.108108108化为分数。
设S = 0.108108108
（1）两边同乘1000得：1000S = 108.108108
（2）（2）-（1）得：999S = 108
从而：S = 108⁄999
2. 对称式计算技巧
解题模型
平方差公式—完全平方公式—整体思想之结合：xy；x-y；xy；22xy中，知二求二。
例子
已知x^2 - y^2 = 8，x + y = 4，求x - y的值。
解：由平方差公式得：(x + y)(x - y) = 8
又因为x + y = 4，所以x - y = 2。
3. 特殊公式
解题模型
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