x-3=y-2=z-1,求x²+y²+z²-xy-yz-zx的值.
问题描述：
x-3=y-2=z-1,求x²+y²+z²-xy-yz-zx的值.
答
x-3=y-2=z-1
x²+y²+z²-xy-yz-zx
=1/2(2x²+2y²+2z²-2xy-2yz-2zx)
=1/2[(x^2-2xy+y^2)+(y^2-2yz+z^2)+(z^2-2zx+x^2)]
=1/2[(x-y)^2+(y-z)^2+(z-x)^2] x-3=y-2z-1 x-y=1y-z=1z-x=-2
=1/2[1+1+4]=3为什么要提½要凑成x-y y-z z-x的完全平方式x-3=y-2=z-1怎么得出x-y=1 y-z=1 z-x=2x-3=y-2x-y=1y-2=z-1 y-z=1x-3=z-1z-x=-2