a^3+b^3+c^3-3abc=0 <=>(a+b)^3 -3ab(a+b) +c^3 - 3abc=0 <=>[(a+b)^3 +c^3] -3ab.(a+b+c)=0 <=>(a+b+c). [(a+b)^2 -c.(a+b)+c^2] -3ab(a+b+c)=0 <=>(a+b+c).(a^2+2ab+b^2-ca-cb+c^2-3ab)... <=>(a+b+c).(a^2+b^2+c^2-ab-bc-ca)=0 luôn đúng do a+b+c=0 (đpcm)
$a^3+b^3+c^3-3abc=0
$ <=>
$(a+b)^3 -3ab(a+b) +c^3 - 3abc=0
$ <=>
$[(a+b)^3 +c^3] -3ab.(a+b+c)=0
$ <=>
$(a+b+c). [(a+b)^2 -c.(a+b)+c^2] -3ab(a+b+c)=0
$<=>
$(a+b+c).(a^2+2ab+b^2-ca-cb+c^2-3ab)...
$<=>
$(a+b+c).(a^2+b^2+c^2-ab-bc-ca)=0
$luôn đúng do a+b+c=0 (đpcm)