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Question

If a, b and c are three positive real numbers, then the minimum value of the expression b+ca+c+ab+a+bc is:

A
1
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B
2
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C
3
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D
6
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Solution

The correct option is C 6
let b+ca,c+ab,a+bc are three positive number, (a,b,c are positive real numbers)

applying property, A.M.G.M.

a+bc+b+ca+c+ab3(1abc(a+b)(b+c)(c+a))13 .......(1)

Applying the same for two numbers a,b and b,c and c,a

(a+b)2ab
(b+c)2bc
(c+a)2ac
from these three we can write,

(a+b)(b+c)(c+a)8abc

putting this value in RHS of eq (1)

minimumum value of G.M.=2

hence from eq (1)

a+bc+b+ca+c+ab32

a+bc+b+ca+c+ab6

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