在数学运算及证明中,有很多解题技巧。掌握了它们,解某些题常能得心应手。如2(x~2+y~2)=(x+y)~2+(x-y)~2(*)就是一个可以利用的恒等式,借助于它,一类题可获得巧妙的解法。下面举例来说明。例1 一个整数可表为两个整数的平方之和,当且仅当这个整数的2倍也有此性质。 There are many problem-solving skills in mathematics operations and certification. Having mastered them, you can often find it easy to solve certain problems. For example, 2(x~2+y~2)=(x+y)~2+(x-y)~2(*) is an identifiable identity. With this, an ingenious solution can be obtained for a class of questions. The following example illustrates. Example 1 An integer can be expressed as the sum of the squares of two integers, if and only if this integer is twice as large.