(a+b+c)²=0=a²+b²+c²+2(ab+ac+bc ) 所以ab+ac+bc=-1/2
a²+b²+c²=1
(ab+bc+ca)^2=(-1/2)^2
a^2b^2+b^2c^2+c^2a^2+2ab*bc+2bc*ca+2ca*ab=1/4
a^2b^2+b^2c^2+c^2a^2+2abc(a+b+c)=1/4
a^2b^2+b^2c^2+c^2a^2=1/4
a²+b²+c²=1
(a²+b²+c²)^2=1
a^4+b^4+c^4+2(a^2b^2+c^2a^2+a^2b^2)=1
a^4+b^4+c^4+2*(1/4)=1
a^4+b^4+c^4=1-(1/2)=1/2