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Prove that (1)/(a) + (1)/(b) + (1)/(c ) ...

Prove that `(1)/(a) + (1)/(b) + (1)/(c ) ge (1)/(sqrt((bc))) + (1)/(sqrt((ca))) + (1)/(sqrt((ab)))`, where a,b,c `gt` 0

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`(1)/(b)+(1)/(c) ge 2[(1)/(b)(1)/(c)]^(1///2)`
`(1)/(a)+(1)/(b) ge 2[(1)/(a)(1)/(b)]^(1//2)`
`(1)/(a)+(1)/(c) ge 2 [(1)/(a)(1)/(c)]^(1//2)`
Adding, we get
`(1)/(a)+(1)/(b)+(1)/(c)ge (1)/(sqrt(bc))+(1)/(sqrt(bc))+(1)/(sqrt(ab))`
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