(1)x²-2x+1/x²+9x-10≥0 (2)3x²-7x/2x²-5x-3≤1
问题描述:
(1)x²-2x+1/x²+9x-10≥0 (2)3x²-7x/2x²-5x-3≤1
答
1)x²-2x+1/x²+9x-10≥0
(x-1)^2/(x²+9x-10≥0
因为(x-1)^2一定≥0
所以(x²+9x-10>0
(x-1)(x+10)>0
x<-10或x>1
2)3x²-7x/2x²-5x-3≤1
当2x²-5x-3<0时,即-1/2<x<3时,原式变为:3x²-7x≤2x²-5x-3,解得(x-1)^2≤-2,无解
当2x²-5x-3>0时,即x>3或x<-1/2时,原式变为:3x²-7x≥2x²-5x-3,解得(x-1)^2≥-2,成立
则x>3或x<-1/2