Question
If a, b, c >0, a + b + c =6 and f(x) = (6x) - 1, find the minimum value of f(a).f(b).f(c)?
Answer: Option D
:
D
f(a).f(b).f(c) = (6−a)(6−b)(6−c)abc = 216−36(a+b+c)+6(ab+bc+ca)−abcabc = (ab+bc+ca)abc - 1 = 6(1a+1b+1c) - 1
As AM≥HM
(1a+1b+1c)3 = 6a+6b+6c3 > 3
6a+6b+6c > 9
f(a).f(b).f(c)> 9 - 1 = 8
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:
D
f(a).f(b).f(c) = (6−a)(6−b)(6−c)abc = 216−36(a+b+c)+6(ab+bc+ca)−abcabc = (ab+bc+ca)abc - 1 = 6(1a+1b+1c) - 1
As AM≥HM
(1a+1b+1c)3 = 6a+6b+6c3 > 3
6a+6b+6c > 9
f(a).f(b).f(c)> 9 - 1 = 8
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