a>b>c,1/a-b+1/b-c≧m/a-c ,求m

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/25 18:40:56
a>b>c,1/a-b+1/b-c≧m/a-c,求ma>b>c,1/a-b+1/b-c≧m/a-c,求ma>b>c,1/a-b+1/b-c≧m/a-c,求m因a>b>c则a-b>0,b-c>0,a-c

a>b>c,1/a-b+1/b-c≧m/a-c ,求m
a>b>c,1/a-b+1/b-c≧m/a-c ,求m

a>b>c,1/a-b+1/b-c≧m/a-c ,求m
因 a>b>c
则 a-b>0,b-c>0,a-c>0
因 1/(a-b)+1/(b-c) ≥ m/(a-c)
(b-c+a-b)/(a-b)(b-c)≥ m/(a-c)
(a-c)^2/(a-b)(b-c)≥m
由基本不等式有
(a-b)(b-c)≤[[(a-b)+(b-c)]/2]^2 = (a-c)^2/4

(a-c)^2/(a-b)(b-c) ≥ 4
所以
m≤4