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计算x-yx+y+y-zy+z+z-xz+x+(x-y)(y-z)(z-x)(x+y)(y+z)(z+x)=（）A.-1B.0C.1D.2
题目详情
计算
+x-y x+y
+y-z y+z
+z-x z+x
=（ ）(x-y)(y-z)(z-x) (x+y)(y+z)(z+x)
A. -1
B. 0
C. 1
D. 2
▼优质解答
答案和解析
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=
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=
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=
-
=0．
故选B．
| x-y |
| x+y |
| y-z |
| y+z |
| z-x |
| z+x |
| (x-y)(y-z)(z-x) |
| (x+y)(y+z)(z+x) |
=
| (x-y)(y+z)(z+x) |
| (x+y)(y+z)(z+x) |
| (y-z)(x+y)(z+x) |
| (x+y)(y+z)(z+x) |
| (z-x)(x+y)(y+z) |
| (x+y)(y+z)(z+x) |
| (x-y)(y-z)(z-x) |
| (x+y)(y+z)(z+x) |
=
| (x-y)(y+z)(z+x) |
| (x+y)(y+z)(z+x) |
| (x-y)(y-z)(z-x) |
| (x+y)(y+z)(z+x) |
| (y-z)(x+y)(z+x) |
| (x+y)(y+z)(z+x) |
| (z-x)(x+y)(y+z) |
| (x+y)(y+z)(z+x) |
=
| 2z(x-y) |
| (y+z)(z+x) |
| 2z(x-y) |
| (y+z)(z+x) |
=0．
故选B．
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