Question

分式不等式小于0的解法

-1<5m-2/2-3m＜1

Answer 1

-1<(5m-2)/(2-3m)<1

解(5m-2)/(2-3m)>-1 ① 且(5m-2)/(2-3m)<1 ②

解①

(5m-2)/(2-3m)+1>0

[(5m-2)+(2-3m)]/(2-3m)>0

2m/(2-3m)>0

m/(3m-2)<0

0<m<2/3

解②

(5m-2)/(2-3m)-1<0

[(5m-2)-(2-3m)]/(2-3m)<0

(8m-4)/(2-3m)<0

(2m-1)/(3m-2)>0

m<1/2或m>2/3

综上所述得不等式的解是：0<x<1/2

基本不等式

①√((a²+b²)/2)≥(a+b)/2≥√ab≥2/(1/a+1/b)

②√(ab)≤(a+b)/2

③a²+b²≥2ab

④ab≤(a+b)²/4

⑤||a|-|b| |≤|a+b|≤|a|+|b|

Answer 2

平方小于一

Answer 3

-1<(5m-2)/(2-3m)<1
解(5m-2)/(2-3m)>-1 ① 且(5m-2)/(2-3m)<1 ②
解①
(5m-2)/(2-3m)+1>0
[(5m-2)+(2-3m)]/(2-3m)>0
2m/(2-3m)>0
m/(3m-2)<0
0<m<2/3
解②
(5m-2)/(2-3m)-1<0
[(5m-2)-(2-3m)]/(2-3m)<0
(8m-4)/(2-3m)<0
(2m-1)/(3m-2)>0
m<1/2或m>2/3
综上所述得不等式的解是：0<x<1/2