Given=(2a+3/a)+(2b+3/b)+(2c+3/c)
A.M.>=G.M.
So (2a+3/a)/2>=sqrt(6) [sqrt-square root]
or (2a+3/a)>=2sqrt(6)
Similarly (2b+3/b)>=2sqrt(6)
and (2c+3/c)>=2sqrt(6)
Adding them we get
(2a+3/a)+(2b+3/b)+(2c+3/c)>=6sqrt(6)
THEREFORE
(a+3/b+c)+(b+3/c+a)+(c+3a+b)>=6sqrt(6)>=14.69
SO THE MINIMUM VALUE IS 6sqrt(6)=14.69
SO THE ANSWER IS 4)NONE OF THESE.
Sir,
please tell me if i'm wrong anywhere