x-3=y-2=z-1,求x²+y²+z²-xy-yz-zx的值.
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x-3=y-2=z-1,求x²+y²+z²-xy-yz-zx的值.
![x-3=y-2=z-1,求x²+y²+z²-xy-yz-zx的值.](/uploads/image/z/15796740-12-0.jpg?t=x-3%3Dy-2%3Dz-1%2C%E6%B1%82x%26%23178%3B%2By%26%23178%3B%2Bz%26%23178%3B-xy-yz-zx%E7%9A%84%E5%80%BC.)
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=1 y-z=1 z-x=-2
=1/2[1+1+4]=3
再问: 为什么要提½
再答: 要凑成x-y y-z z-x的完全平方式
再问: x-3=y-2=z-1怎么得出x-y=1 y-z=1 z-x=2
再答: x-3=y-2 x-y=1 y-2=z-1 y-z=1 x-3=z-1 z-x=-2
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=1 y-z=1 z-x=-2
=1/2[1+1+4]=3
再问: 为什么要提½
再答: 要凑成x-y y-z z-x的完全平方式
再问: x-3=y-2=z-1怎么得出x-y=1 y-z=1 z-x=2
再答: x-3=y-2 x-y=1 y-2=z-1 y-z=1 x-3=z-1 z-x=-2
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