将题中等式移项并将等号两边同乘以2得：x-2

x

+y-2

y-1

+z-2

z-2

=0

配方得(x-2

x

+1)+(y-1-2

y-1

+1)+(z-2-2

z-2

+1)=0

∴(

x

-1)2+(

y-1

-1)2+(

z-2

-1)2=0

∴

x

=1且

y-1

=1且

z-2

=1

解得  x=1   y-2   z=3

∴（x-yz）²=（1-2×3）²=25