Question

不等式（x+5)/(x-1)²≥2的解集是多少？

Answer 1

(x+5)/(x-1)²≥2
(x+5)/(x-1)²-2≥0
[(x+5)-2(x-1)²]/(x-1)²≥0
(x+5)-2(x-1)²≥0且x≠1
2x²-5x-3≤0且x≠1
(x-3)(2x+1)≤0且x≠1
-1/2≤x≤3且x≠1

所以解集是{x|-1/2≤x≤3且x≠1}

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Answer 2

（x+5)/(x-1)²≥2
(x+5)/(x-1)²-2≥0
[x+5-2(x-1)²]/(x-1)²≥0
(-2x²+5x+3)/(x-1)²≥0
(2x+1)(-x+3)/(x-1)²≥0
则(2x+1)(-x+3)≥0且x-1≠0
则(2x+1)(x-3)≤0且x≠1
则-1/2≤x≤3且x≠1
所以解集是-1/2≤x<1或1<x≤3

Answer 3

解集为｛x／1＜x小于等于3／2｝

Answer 4

(x+5)/(x-1)²≥2
x+5≥2(x-1)²
x+5≥2x²-4x+2
2x²-5x-3≤0
1 -3
2 1
(x-3)(2x+1)≤0
-1/2≤x≤3 x≠1