a+b+c=1
1/a+1/b+1/c
=(a+b+c)/a+(a+b+c)/b+(a+b+c)/c
=3+(a/b+b/a)+(a/c+c/a)+(b/c+c/b)
而a.b.c∈R*，那么a/b>0 b/c>0 a/c>0
a/b+b/a>=2√(a/b*b/a)=2
a/c+c/a>=2√(a/c*c/a)=2
b/c+c/b>=2√(b/c*c/b)=2
所以1/a+1/b+1/c=3+(a/b+b/a)+(a/c+c/a)+(b/c+c/b)>=3+2+2+2=9
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