已知A+B+C=0 A^2+ B^2+ C^2=4 A^4+B^4+C^4=??

(A+B+C)²=A^2+ B^2+ C^2+2(AB+AC+BC)=4+2(AB+AC+BC)=0
=>AB+AC+BC=-2
=>(AB+AC+BC)²=A²B²+A²C²+B²C²+2(AB.AC+AC.BC+BC.AB)=4
=>A²B²+A²C²+B²C²+2ABC(A+B+C)=A²B²+A²C²+B²C²=4
=>A^4+B^4+C^4=16-2(A²B²+A²C²+B²C²)=8

A + B + C = 0
(A + B + C)² = 0
A² + B² + C² + 2AB + 2BC + 2AC = 0
4 + 2AB + 2BC + 2AC = 0
2AB + 2BC + 2AC = -4
AB + BC + AC = -2
(AB + BC + AC)² = 4
A²B² + B²C² + A²C² + 2A²BC + 2AB²C + 2ABC² = 4
A²B² + B²C² + A²C² + 2ABC(A+B+C) = 4
A²B² + B²C² + A²C² = 4

A² + B² + C² = 4
(A² + B² + C²)² = 16
A^4 + B^4 + C^4 + 2A²B² + 2B²C² + 2A²C² = 16
A^4 + B^4 + C^4 + 2(4) = 16
A^4 + B^4 + C^4 = 8

8