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在有几个变元的问题中,常常有一个(或几个)变元处于主要地位,我们不妨称之为主元。由于思维定势的影响,人们在解决这一类型问题时,总是紧紧抓住主元不放,这在很多情况下是正确的。但在某些情况下,如果我们变更主元,即把某个处于次要地位的变元突出出来,常常能取得出人意料的效果。例1 已知方程ax~2-2(a-3)x+a-2=0中的α为负整数,试求出那些能使此方程的解x至少有一个为整数时α的值。很多人在解决这一问题时,由于定势影
In a problem with several arguments, there is often one (or several) argument that is in a dominant position, and we may call it pivotal. Due to the influence of mindset, people always hold onto the main element when they solve this type of problem. This is correct in many cases. But in some cases, if we change the main element, that is to highlight a subordinated variable, we can often achieve surprising results. Example 1 Knowing that α is a negative integer in the equation ax~2-2(a-3)x+a-2=0, try to find the values of α that make the solution x of this equation at least one integer. When many people are solving this problem, due to the constant influence