已知a+b+c=0,求a^2+b^2+c^2+2ab+2bc+2ac是多少?

问题描述:

已知a+b+c=0,求a^2+b^2+c^2+2ab+2bc+2ac是多少?

0啊

a^2+b^2+c^2+2ab+2bc+2ac
=(a+b+c)^2
=0

... 0

a^2+b^2+c^2+2ab+2bc+2ac
=(a+b+c)^2
=0

a^2+b^2+c^2+2ab+2bc+2ac
=(a^2+b^2+2ab)+c^2+(2ac+2bc)
=(a+b)^2+2c(a+b)+c^2
=(a+b+c)^2
=0