解不等式3/x≦1:
3/x≦1⇒x*(3/x)≦x*1⇔3≦x，故x≧3
請問哪裡錯了？
要怎麼〝 去分母〞（兩邊乘上x)運算？
高一數學 簡易分式不等式?
2015-09-13 5:41 am
回答 (2)
2015-09-13 6:24 am
分母不知正負所以不能兩邊同乘x
3/x<=1 ,x不等於0
==>(3/x)-1<=0
==>(3-x)/x<=0
==>(3-x)x<=0
==>x(x-3)>=0
==>x>=3或x<=0 (因x不等於0要去除)
==>x>=3或x<0
3/x<=1 ,x不等於0
==>(3/x)-1<=0
==>(3-x)/x<=0
==>(3-x)x<=0
==>x(x-3)>=0
==>x>=3或x<=0 (因x不等於0要去除)
==>x>=3或x<0
2015-09-13 6:20 am
解不等式3/x<=1
Sol
提供作法錯誤
x>0
x*(3/x)<=x*1
3<=x.................
x<0
(3/x)<=1恆真
x<0..................
or
3/x<=1
x<>0
3/x－1<=0，x<>0
3/x－x/x<=0，x<>0
(3－x)/x<=0，x<>0
(3－x)x<=0，x<>0
(x－3)x>=0，x<>0
(x<=0 or x-3>=0)，x<>0
(x<=0，x<>0) or(x>=3，x<.0)
x<0 or x>=3
Sol
提供作法錯誤
x>0
x*(3/x)<=x*1
3<=x.................
x<0
(3/x)<=1恆真
x<0..................
or
3/x<=1
x<>0
3/x－1<=0，x<>0
3/x－x/x<=0，x<>0
(3－x)/x<=0，x<>0
(3－x)x<=0，x<>0
(x－3)x>=0，x<>0
(x<=0 or x-3>=0)，x<>0
(x<=0，x<>0) or(x>=3，x<.0)
x<0 or x>=3
收錄日期: 2021-04-30 19:50:15
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150912214147AAdOOHB