已知a>b>c,求证:1/a-b+1/b-c大于等于4/a-c,

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已知a>b>c,求证:1/a-b+1/b-c大于等于4/a-c,
已知a>b>c,求证:1/a-b+1/b-c大于等于4/a-c,

已知a>b>c,求证:1/a-b+1/b-c大于等于4/a-c,
a>b,a-b>0
1/(a-b)>0
b>c,b-c>0
1/(b-c)>0
a>c,a-c>0
1/(a-c)>0
1/(a-b)+1/(b-c)+1/(a-c)>0

a>b,a-b>0
1/(a-b)>0
b>c,b-c>0
1/(b-c)>0
a>c,a-c>0
1/(a-c)>0
1/(a-b)+1/(b-c)+1/(a-c)>0

1/(a-b)+1/(b-c)-4/(a-c)
=(a-c)/(a-b)(b-c)- 4/(a-c)
={(a-c)^2-(a-b)(b-c)}/(a-b)(b-c)(a-c)
={(a+c)^2-4b(a+c)+4b^2}/(a-b)(b-c)(a-c)
=(a+c-2b)^2/(a-b)(b-c)(a-c)>=0
1/(a-b)+1/(b-c)>=4/(a-c)