Question

不等式x+5/(x-1)^2>=2的解集是

Answer 1

x+5/(x-1)²≥2

(x-1)²作为分母是大于0的
所以化简得：
x+5≥2(x-1)²
x+5≥2x²-4x+2
2x²-5x-3≤0
(2x+1)(x-3)≤0
-1/2≤x≤3
且x-1≠0
x≠1

所以解集为[-1/2,1)∪(1,3]

追问

实数x，y满足不等式x+3y-3=0，y>.=0,则ω=y-1/x+1的取值范围是

Answer 2

x+5/(x-1)^2>=2
x+5>=2(x-1)^2
x+5>=2x^2-4x+2
2x^2*5x-3<=0
(2x+1)(x-3)<=0
-1/2<=x<=3
即不等式的解集是x大于等于-1/2且小于等于3