若x-3=y-2=z-1求x²+y²+z²-xy-yz-zx的值.

x-3=y-2
x-y=1
y-2=z-1
y-z=1
x-3=z-1
z-x=-2
x^2+y^2+z^2-xy-yz-xz
=x(x-y)+y(y-z)+z(z-x)
=x+y-2z
x-3=z-1
y-2=z-1
2式相加,得
x+y-5=2z-2
x+y-2z=3
原式=3