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If a, b, c are positive real number such...

If a, b, c are positive real number such that `lamba` abc is the minimum value of `a(b^(2)+c^(2))+b(c^(2)+a^(2))+c(a^(2)+b^(2))`, then `lambda`=

A

1

B

2

C

3

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
Using `A.M.geG.M.`, we have
`(a(b^(2)+c^(2))+b(c^(2)+a^(2))+c(a^(2)+b^(2)))/(6)ge(ab^(2)ac^(2)bc^(2)ba^(2)ca^(2)cb^(2))^(1//6)`
`implies" "(a (b^(2)+c^(2))+b(c^(2)+a^(2))+c(a^(2)+b^(2)))/(6)geabc`
`implies" "a(b^(2)+c^(2))+b(c^(2)+a^(2))+c(a^(2)+b^(2))ge6abc`
`implies" "lambda=6`
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