max value
if a+2b+c=4 then what is the maxm value of ab+bc+ca
my first thought was applying am gm with (a+b) and (b+c)
ultimately giving ab+bc+ca+b^2<=4
now, the answer is 4 which can be achieved by putting b^2=0 but thats only possible when b=0 thus giving max value of ac=4. so is it mathematically correct to say max(ab+bc+ca) = 4 even when b=0
my first thought was applying am gm with (a+b) and (b+c)
ultimately giving ab+bc+ca+b^2<=4
now, the answer is 4 which can be achieved by putting b^2=0 but thats only possible when b=0 thus giving max value of ac=4. so is it mathematically correct to say max(ab+bc+ca) = 4 even when b=0
