Question

一道关于解不等式的数学题、求解答案

解不等式｜x+1/x-1｜≤1
需要详细解答过程

Answer 1

(x+1)/(x-1)|≤1 <==>
-1≤(x+1)/(x-1)≤1 <==>
{(x+1)/(x-1)≤1, (x+1)/(x-1)>=-1} <==>
{2/(x-1)≤0, 2x/(x-1)>=0} <==>
x=<0。
即原不等式的解集为{x| x=<0}。

Answer 2

x<1

Answer 3

-1≤x+1/x-1≤1，0≤x+1/x≤2，所以x>=0，另x+1/x>=2，所以x+1/x=2，所以x=1

Answer 4

∵｜x+1/x-1｜≤1
∴-1≤x+1/x-1≤1
∴0≤x+1/x≤2
∵0≤x+1/x 推得X ＞0
x+1/x≤2 推得X=1
∴ X=1