a b c同号且互不相等,a+b+c=1,求证1/a+1/b+1/c>9

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a b c同号且互不相等,a+b+c=1,求证1/a+1/b+1/c>9
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a b c同号且互不相等,a+b+c=1,求证1/a+1/b+1/c>9
a b c同号且互不相等,a+b+c=1,求证1/a+1/b+1/c>9

a b c同号且互不相等,a+b+c=1,求证1/a+1/b+1/c>9
1/a+1/b+1/c=(a+b+c)/a+(a+b+c)/b+(a+b+c)/c=(1+b/a+c/a)+(1+a/b+c/b)+(1+a/c+b/c)=3+(a/b+b/a)+(b/c+c/b)+(c/a+a/c)≥3+2+2+2≥9(当a=b=c时取等号).
所以1/a+1/b+1/c>9