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Re: Maximum / Minimum type of questions
by Kuntal Roy - Wednesday, 22 April 2015, 10:02 AM
  (b^2 + c^2) >= (b ^2 .c ^2) (using AM>=GM for positive real numbers  )
or , (b^2 + c^2) >= bc
similarly (a^2 + b^2) >= ab
(a^2 + c^2) >= ca

hence ab+bc+ca <= (a^2 +b^2 + c^2) = 48

again (a+b+c)^2= (a^2 +b^2 + c^2) + 2(ab+bc+ca)

(a+b+c)^2= 48 + 2(ab+bc+ca)

now (a+b+c)^2 is max when (ab+bc+ca) is max

hence maximum value of (a+b+c)^2  = 48+2x48= 144

again since a,b,c are real and positive a+b+c is max when (a+b+c)^2 is max

hence maximum value of (a+b+c) is = sqrt(144) =12