问题
解答题
已知x+y+z=1,x2+y2+z2=2,x3+y3+z3=3,求
|
答案
∵(x+y+z)2=x2+y2+z2+2(xy+yz+xz),
即9=7+2(xy+yz+xz),
∴xy+yz+xz=-
,1 2
x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx),
即3-3xyz=2+
,1 2
∴xyz=
,1 6
+1 x
+1 y
=1 z
=-3,xy+yz+xz xyz
故答案为-3.