Question

若a,b,c均大于0,证明不等式3(1/a +1/b+ 1/c)^（-1）<=(abc)ˇ3？

用条件极值求

Answer 1

a,b,c均大于0，
所以1/a+1/b+1/c>=3[1/(abc)]^(1/3)>0,
所以(1/a+1/b+1/c)^(-1)<=1/{3[1/(abc)]^(1/3)]=(1/3)(abc)^(1/3),
所以3(1/a+1/b+1/c)^(-1)<=(abc)^(1/3).
题目有误。