初始数学衔接问题
已知a+b+c=0 a?+b?+c?=1所以(a+b+c)?=0
答?+b?+c?+2(a b+AC+BC)= 0 1+2(a b+AC+BC)= 0所以ab+ac+bc=-1/2 (ab+ac+bc)?=1/4,也就是a?b?+a?c?+b?c?+2(a?bc+b?ac+c?ab)=1/4 a?b?+a?c?+b?c?+2abc(a+b+c)=1/4(称为a+b+c=0)
所以a?b?+a?c?+b?c?=1/4,
(a?+b?+c?)?=a^4+b^4+c^4+2 a?b?+2a?c?+2b?c?
=a^4+b^4+c^4+2(a?b?+a?c?+b?c?)
所以a 4+b 4+c 4 = (a?+b?+c?)?- 2(a?b?+a?c?+b?c?)=1- 2*(1/4)=1-(1/2)=1/2
(a?+b?+c?=1,a?b?+a?c?+b?c?=1/4 )
最后的答案是1/2