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已知x-y=m,y-z=n.求x^2+y^2+z^2-xy-yz-xz
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已知x-y=m,y-z=n.求x^2+y^2+z^2-xy-yz-xz
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答案和解析
x-z=m+n
x^2+y^2+z^2-xy-yz-xz
=0.5*2*(x^2+y^2+z^2-xy-yz-xz)
=0.5*(x^2-2xy+y^2+y^2-2yz+z^2+x^2-2xz+z^2)
=0.5*((x-y)^2+(y-z)^2+(x-z)^2)
=0.5*(m^2+n^2+(m+n)^2)
=m^2+n^2+m*n
x^2+y^2+z^2-xy-yz-xz
=0.5*2*(x^2+y^2+z^2-xy-yz-xz)
=0.5*(x^2-2xy+y^2+y^2-2yz+z^2+x^2-2xz+z^2)
=0.5*((x-y)^2+(y-z)^2+(x-z)^2)
=0.5*(m^2+n^2+(m+n)^2)
=m^2+n^2+m*n
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