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

考點：分式的化簡求值

專題：計算題

分析：由已知等式求出k的值，即可確定出原式的值．

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，
則k¹+k²+k³=1+1+1=3．

點評：此題考查了分式的化簡求值，熟練掌握運算法則是解本題的關鍵．