x-3=y-2=z-1,求x^2+y^2+z^2-xy-yz-xz的值

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x-3=y-2=z-1,求x^2+y^2+z^2-xy-yz-xz的值
x-3=y-2=z-1,求x^2+y^2+z^2-xy-yz-xz的值

x-3=y-2=z-1,求x^2+y^2+z^2-xy-yz-xz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-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

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

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