有关“至少存在问题”,一般都用反证法证明。这里,我们介绍一种直接证法——变更命题法。这种证法思路灵活,解法简捷。下面从三个方面来举例说明。一、变更为等价命题变更的目的,首先是使问题明朗化,从而便于寻求解题途径或者简化解题过程。例1 若下列三个方程中至少有一个方程有实数解,求实数a的范围。x~2+4ax-4a+3=0,x~2+(a-1)x+a~2=0,x~2+2ax-2a=0。变更:由于“三个二次方程中至少有一个 Regarding “at least a problem”, it is generally proved by counter-evidence. Here, we introduce a direct proof-change proposition method. This method of proof is flexible and simple to solve. Here are three examples to illustrate. First, to change the purpose of the change of the equivalent proposition, the first is to clarify the problem, so as to facilitate the search for a solution to the problem or simplify the problem-solving process. Example 1 If the at least one of the following three equations has a real solution, find the range of the real number a. x~2+4ax-4a+3=0, x~2+(a-1)x+a~2=0, and x~2+2ax-2a=0. Change: Due to "at least one of the three quadratic equations