PF1+PF2=8,∴PF2=8-PF1,代入原式,就是[2PF1-8]/PF1,分类讨论,去掉绝对值就行了
|PF1?PF2|PF1=|PF1?(8?PF1)|PF1=|PF1?(8?PF1)PF1|=|2?8PF1|,因为2≤PF1≤6且函数y=2?8x在x∈[2,6]上单调递增,所以?2≤2?8PF1≤23,故|2?8PF1|∈[0,2].故答案为:[0,2].
答案为,[0,2]