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

一道有点味儿的数学题目，谁来啃啃啊？加油吧！谢谢各位的热情！

Answer 1

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=1 y^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

一楼是对的 建议分给一楼 他最快

Answer 2

=4(x+y+z)
=4*1
=4

Answer 3

^是什么意思