設x,y為實數，|x-1|≤5,|y+1|≤3,則|2x+9|-|x+7|+|x+y-19|+|y+8|之值?
回答 (1)
2016-08-02 11:39 pm
Sol
｜x－1｜<=5
－5<=x－1<=5
－4<=x<=6
－8<=2x<=12
1<=2x+9<=21
｜2x+9｜=2x+9
3<=x+7<=13
｜x+1｜=x+7
｜y+1｜<=3
－3<=y+1<=3
－4<=y<=2
－8<=x+y<=8
－27<=x+y－19<=－11
｜x+y－19｜=－x－y+19
4<=y+8<=10
｜y+8｜=y+9
So
｜2x+9｜－｜x+7｜+｜x+y－19｜+｜y+8｜
=(2x+9)－(x+7)+(－x－y+19)+(y+8)
=29
｜x－1｜<=5
－5<=x－1<=5
－4<=x<=6
－8<=2x<=12
1<=2x+9<=21
｜2x+9｜=2x+9
3<=x+7<=13
｜x+1｜=x+7
｜y+1｜<=3
－3<=y+1<=3
－4<=y<=2
－8<=x+y<=8
－27<=x+y－19<=－11
｜x+y－19｜=－x－y+19
4<=y+8<=10
｜y+8｜=y+9
So
｜2x+9｜－｜x+7｜+｜x+y－19｜+｜y+8｜
=(2x+9)－(x+7)+(－x－y+19)+(y+8)
=29
收錄日期: 2021-04-30 20:28:46
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160802062920AAAWeo3