If a>0, b>0, c>0 and the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is abc then is

JEE Advanced Mathematics question

Mathematics Application of Derivatives JEE Advanced

If and the minimum value of

+++++

is then is

(A)2
(B)1
(C)6Correct
(D)3

Answer: (C)

Solution

The expression is the sum of six positive terms ab^2, ac^2, bc^2, ba^2, ca^2, cb^2. Their product is (each letter appears with total exponent 6), so their GM is

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Question ID VK-107837