已知三个数x,y,z满足xy/x+y=-2,yz/y+z=4/3,zx/z+x=-4/3.求xyz/xy+yz+zx的值.
问题描述:
已知三个数x,y,z满足
=-2,xy x+y
=yz y+z
,4 3
=-zx z+x
.求4 3
的值. xyz xy+yz+zx
答
∵
=-2,xy x+y
=yz y+z
,4 3
=-zx z+x
,4 3
∴
+1 x
=-1 y
,1 2
+1 y
=1 z
,3 4
+1 z
=-1 x
,3 4
∴2(
+1 x
+1 y
)=-1 z
,即1 2
+1 x
+1 y
=-1 z
,1 4
则
=xyz xy+yz+zx
=-4.1
+1 x
+1 y
1 z