由题意(x+y+z)^3=1

　　x^3+y^3+z^3+2x^2(y+z)+2z^2(x+y)+2y^2(x+z)+3xyz=1

　　整理得xyz=0

　　不妨设x=0

　　又xy+yz+xz=0.5[(x+y+z)^2-(x^2+y^2+z^2)]=-0.5

　　则y+z=1y^3+z^3=1

　　y^4+z^4=(y+z)(y^3+z^3)-yz(y^2+z^2)=4

　　故x^4+y^4+z^4=4