已知a+b+c=1求证(1/a-1)(1/b-1)(1/c-1)大于等于8
1个回答
2013-11-02
展开全部
(1/a-1)(1/b-1)(1/c-1)=( a+b+c/a-1)(a+b+c/b-1)(a+b+c/c-1)
=(1+b/a+c/a-1)(a/b+1+c/b-1)(a/c+b/c+1-1)
=(b/a+c/a)(a/b+c/b)(a/c+b/c)
>=2根号bc/a2*2根号ac/b2*2根号ab/c2
=8
=(1+b/a+c/a-1)(a/b+1+c/b-1)(a/c+b/c+1-1)
=(b/a+c/a)(a/b+c/b)(a/c+b/c)
>=2根号bc/a2*2根号ac/b2*2根号ab/c2
=8
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