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Question

If a,b,c be positive, then minimum value of b+ca + c+ab + a+bc is __

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Solution

Since Arithmetic mean Geometric mean

ab+ba2 ab.ba

ab+ba 2 -----------------(1)

Similarly, bc+cb 2 ------------------(2)

and ca+ac 2 -------------------(3)

Adding the corresponding sides of (1),(2) and (3),

(ab+ba) + (bc+cb) + (ca+ac) 6

(or) (ba+ca) + (cb+ab) + (ac+bc) 6

b+ca + c+ab + a+bc 6

So, the minimum value is 6.


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