設a.b均為實數，若絕對值不等式丨x/a +1丨小於等於b/a的解的範圍是-1~4(-1和4包含在內)，求數對a.b為?
回答 (1)
2017-07-13 7:22 pm
Sol
｜x/a+1｜<=b/a
－b/a<=x/a+1<=b/a
(1) a>0
－b/a<=x/a+1<=b/a
－b<=x+a<=b
－a－b<=x<=－a+b
－a－b=－1
－a+b=4
－2a=3
a=－3/2
無解
(2) a<0
－b/a<=x/a+1<=b/a
－b>=x+a>=b
b<=x+a<=－b
－a+b<=x<=－a－b
－a+b=－1
－a－b=4
－2a=3a
a=－3/2
b=1/2
(a，b)=(－3/2，1/2)
｜x/a+1｜<=b/a
－b/a<=x/a+1<=b/a
(1) a>0
－b/a<=x/a+1<=b/a
－b<=x+a<=b
－a－b<=x<=－a+b
－a－b=－1
－a+b=4
－2a=3
a=－3/2
無解
(2) a<0
－b/a<=x/a+1<=b/a
－b>=x+a>=b
b<=x+a<=－b
－a+b<=x<=－a－b
－a+b=－1
－a－b=4
－2a=3a
a=－3/2
b=1/2
(a，b)=(－3/2，1/2)
收錄日期: 2021-04-30 22:07:24
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170713094923AAiNILX