basic

• June 26th 2009, 09:12 AM
abhishek arora
basic
let a,b,c real no's such that a+2b+c=4 then find max value of (ab + bc + ac)

(ans=4)
• June 26th 2009, 10:12 AM
TheAbstractionist
$a+2b+c=4\,\implies\,b=\frac{4-(a+c)}2$

If you substitute this into $ab+bc+ca$ and simplify, I think you should get

$ab+bc+ca\ =\ 4-\frac{(a-2)^2}2-\frac{(c-2)^2}2$

Hence $ab+bc+ca\,\le\,4$ for all $a,b,c\in\mathbb R.$
• June 26th 2009, 10:25 AM
abhishek arora
favour
sir can you please add the simplification part actually i could not manage to get to the simplified form
• June 26th 2009, 11:56 AM
TheAbstractionist
$ab+bc+ca\,=\,b(a+c)+ac$

$=\,\frac{(4-(a+c))(a+c)}2+ac$

$=\,\cdots$

Carry on from there.