Question

已知a,b,c∈R,且a+b+c=1,求证:1/a+1/b+1/c≥9

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Answer 1

1/a+1/b+1/c
=(a+b+c)/a+(a+b+c)/b+(a+b+c)/c
=1+(b+c)/a+1(a+c)/b+1(a+b)/c
=3+b/c+c/b+a/c+c/a+a/b+b/a （由于b/a+a/b>=2，c/a+a/c>=2，c/b+b/c>=2）
>=3+2+2+2
=9