问题
解答题
已知实数x，y，z满足
|
答案
∵
+x y+z
+y z+x
=1，z x+y
∴
=1-（x y+z
+y z+x
），z x+y
=1-（y z+x
+x y+z
），z x+y
=1-（z x+y
+x y+z
），y z+x
∴
+x2 y+z
+y2 z+x
=x•z2 x+y
+y•x y+z
+z•y z+x z x+y
=x•[1-（
+y z+x
）]+y•[1-（z x+y
+x y+z
）]+z•[1-（z x+y
+x y+z
）]y z+x
=x-
-xy z+x
+y-xz x+y
-xy y+z
+z-yz x+y
-xz y+z yz z+x
=x+y+z-
-xy+yz z+x
-xz+yz x+y xy+xz y+z
=x+y+z-y-z-x
=0．