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Q.

 Ifa,b,c∈R+and a2bc+4abc+4bc=81 such that(2a+b+c+4) assumes its least value, then select the correct alternative/s

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a

b=3a

b

b≤c

c

The value of (a+b+c) is a prime number

d

The value ofabc  is a prime number

answer is A, C, D.

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Detailed Solution

bc(a2+4a+4)=81⇒bc(a+2)2=81

(a+2)+(a+2)+b+c4≥[(a+2)2bc]1/4

2a+b+c+4≥12

Equality occurs when  a+2=b=c=3.⇒a=1,b=3,c=3

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