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Question

If a,b,c are three distinct positive real number , then the least value of
(1+a+a2)(1+b+b2)(1+c+c2)abc, is

A
3
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B
9
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C
27
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D
None of the above.
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Solution

The correct option is C 27
since, A.M.G.M.

a+b+c33abc

let a=1,b=a and c=a2

1+a+a2331aa2

1+a+a23a

1+a+a2a3 ------(1)

similarly,
1+b+b2b3------(2)
and
1+c+c2c3------(3)

multiplying (1), (2) and (3) we get

(1+a+a2a)(1+b+b2b)(1+c+c2c)333

(1+a+a2)(1+b+b2)(1+c+c2)abc27


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