Question

已知

y+z-x

x+y-z

=

z+x-y

y+z-x

=

x+y-z

z+x-y

=k，求k¹+k²+k³的值．

Answer 1

考点：分式的化简求值

专题：计算题

分析：由已知等式求出k的值，即可确定出原式的值．

解答：解：∵

y+z-x

x+y-z

=

z+x-y

y+z-x

=

x+y-z

z+x-y

=k，
∴k³=

y+z-x

x+y-z

•

z+x-y

y+z-x

•

x+y-z

z+x-y

=1，
∴k=1，k²=1，
则k¹+k²+k³=1+1+1=3．

点评：此题考查了分式的化简求值，熟练掌握运算法则是解本题的关键．