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Question

If a,b,c R+ and a2bc+4abc+4bc=81 such that (2a+b+c+4) assumes its least value, then

A
a is a prime number
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B
a+b+c is a prime number
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C
b+ca is a prime number
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D
a3+b3+c3 is a product of two prime numbers
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Solution

The correct option is D a3+b3+c3 is a product of two prime numbers
bc(a2+4a+4)=81
bc(a+2)2=81

AM GM
(a+2)+(a+2)+b+c4[(a+2)2bc]14
2a+b+c+412
equality holds when a+2=b=c=3
a=1, b=3, c=3

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