Question

已知x+y+z=1,x^2+y^2+z^2=2,x^3+y^3+z^3=3,求x^4+y^4+z^4

Answer 1

由题意(x+y+z)^3=1x^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=1 y^3+z^3=1y^4+z^4=(y+z)(y^3+z^3)-yz(y^2+z^2)=4故x^4+y^4+z^4=4一...