已知a,b,c,都属于正实数,且a+b+c=1,求｛（1/a）-1｝*｛（1/b）-1｝*｛（1/c）-1｝的最小值

已知a,b,c,都属于正实数,且a+b+c=1
所以[1/a-1]*[1/b-1]*[1/c-1]
=[(a+b+c)/a-1]*[(a+b+c)/b-1]*[(a+b+c)/c-1]
=[b/a+c/a]*[a/b+c/b]*[a/c+b/c]
=[1+c/a+c/b+c^2/ab]*[a/c+b/c]
=a/c+b/c+1+b/a+a/b+1+c/b+c/a
=2+a/c+c/a+b/a+a/b+b/c+c/b
≥2+2√[(a/c)*(c/a)]+2√[(b/a)*(a/b)]+2√[(b/c)*(c/b)]
=2+6
=8