文[1]和文[2]分别给出了2006年安徽省高中数学竞赛初赛中的题目:“设x,y是实数,且满足x~2+xy+y~2=3.则x~2-xy+y~2的最大值和最小值是__.”的三种思路三种解法与二种思路三种解法.笔者拜读了之后颇有感想,下面给出这个题目的一个变式,供大家参考.由于xy=x~2·y/x,y~2=xy·y/x,于是我们可 Articles [1] and [2] respectively give the questions in the 2006 Anhui Senior High School Mathematical Contest Preliminary: “Set x and y to be real numbers and satisfy x~2+xy+y~2=3. Then x~ The maximum and minimum value of 2-xy+y~2 is __.” Three ways of thinking Three kinds of solutions and two kinds of ideas Three kinds of solutions. The author read quite a lot of thoughts, the following gives a change of this topic For your reference, because xy=x~2·y/x,y~2=xy·y/x, then we can