a+b+c=0
c=-(a+b)
ab+bc+ca
=ab+c(a+b)
=ab-(a+b)^2
(a+b)^2≥4|ab|
ab+bc+ca≤ab-4|ab|≤|ab|-4|ab|=-4|ab|≤0
ab+bc+ca≤0
已知a+b+c=0,求证；ab+bc+ca
a+b+c=0
c=-(a+b)
ab+bc+ca
=ab+c(a+b)
=ab-(a+b)^2
(a+b)^2≥4|ab|
ab+bc+ca≤ab-4|ab|≤|ab|-4|ab|=-4|ab|≤0
ab+bc+ca≤0