一道有点难度的题,尽快解决已知X=2005A+2004Y=2005A+2005Z=2005A+2006则X^2+Y^2+Z^2-XY-YZ-XZ的值是?这个题是擂台赛的.回答的好追加分,谢谢

Question

一道有点难度的题,尽快解决
已知X=2005A+2004
Y=2005A+2005
Z=2005A+2006
则X^2+Y^2+Z^2-XY-YZ-XZ的值是?
这个题是擂台赛的.回答的好追加分,谢谢

Answer 1

X=2005A+2004
Y=2005A+2005
Z=2005A+2006
x-y=-1
y-z=-1
x-z=-2
X^2+Y^2+Z^2-XY-YZ-XZ
=(x^2-2xy+y^2+x^2-2xz+z^2+y^2-2yz+z^2)/2
=[(x-y)^2+(x-z)^2+(y-z)^2]/2
=(1+1+4)/2
=3