# Math Help - basic

1. ## basic

let a,b,c real no's such that a+2b+c=4 then find max value of (ab + bc + ac)

(ans=4)

2. $a+2b+c=4\,\implies\,b=\frac{4-(a+c)}2$

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 $a,b,c\in\mathbb R.$

3. ## favour

sir can you please add the simplification part actually i could not manage to get to the simplified form

4. $ab+bc+ca\,=\,b(a+c)+ac$

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

$=\,\cdots$

Carry on from there.