已知a,b,c属于R+,a+b+c=1,求证(1/a-1)(1/b-1)(1/c-1)>=8
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已知a,b,c属于R+,a+b+c=1,求证(1/a-1)(1/b-1)(1/c-1)>=8
已知a,b,c属于R+,a+b+c=1,求证(1/a-1)(1/b-1)(1/c-1)>=8
已知a,b,c属于R+,a+b+c=1,求证(1/a-1)(1/b-1)(1/c-1)>=8
1/a-1=(a+b+c)/a-1=b/a+c/a
1/b-1=(a+b+c)/b-1=a/b+c/b
1/c-1=(a+b+c)/c-1=a/c+b/c
(1/a-1)(1/b-1)(1/c-1)≥2√(b/a*c/a)×2√(a/b*c/b)×2√(a/c*b/c)=8