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If a ,b ,c in R^+, t h e n(b c)/(b+c)+(...

If `a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b)` is always `lt=1/2(a+b+c)` `geq1/3sqrt(a b c)` `lt=1/3(a+b+c)` `geq1/2sqrt(a b c)`

A

`le (1)/(2)(a+b+c)`

B

`ge (1)/(2)sqrt(abc)`

C

`le (1)/(3)(a+b+c)`

D

`ge (1)/(2)sqrt(abc)`

Text Solution

Verified by Experts

The correct Answer is:
A
Using A.M and H.M inequalit, we get
`(2 bc)/(b + c) le (b + c)/(2), (2 ac)/(a + c) le (a + c)/(2), (2ab)/(a + b) le (a + b)/(2)`
Adding, `(bc)/(b + c) + (ac)/(a + c) + (ab)/(a + b) le (1)/(2) (a + b + c)`
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