正数abc
ab/c+bc/a+ca/b=
(a^2b^2+b^2c^2+c^2a^2)/abc
=[(a^2b^2+c^2)+(a^2b^2+b^2c^2)+(b^2c^2+c^2a^2)]/2abc
=[a^2(b^2+c^2)+b^2(a^2+c^2)+c^2(b^2+a^2)]/2abc
≥(2bc*a^2+2ac^b^2+2ba^c^2)/2abc=a+b+c=3a=3b=3c
即当且仅当a=b=c时有最小值3a或3b或3c
将a=b=c代入已知条件,得a=b=c=√2
所以最小值为3√2