若x-3=y-2=z-1求x²+y²+z²-xy-yz-zx的值.

若x-3=y-2=z-1求x²+y²+z²-xy-yz-zx的值.
若x-3=y-2=z-1求x²+y²+z²-xy-yz-zx的值.

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

x-y=1
y-z=1
z-x=-2
x²+y²+z²-xy-yz-zx
=1/2*(x^2-2xy+y^2+y^2-2yz+z^2+z^2-2xz+x^2)
=1/2*((x-y)^2+(y-z)^2+(z-x)^2)
=1/2*(1^2+1^2+(-2)^2)
=3

x-3=y-2=z-1,
x-y=1
y-z=1
z-x=-2
x^2+y^2+z^2-xy-yz-xz
=(1/2)*[(x-y)^2+(y-z)^2+(z-x)^2]
=(1/2)*(1+1+4)
=(1/2)*6
=3