已知:x-y=5,z-y=3,求x^2+y^2+z^2-xy-yz-xz的值
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![已知:x-y=5,z-y=3,求x^2+y^2+z^2-xy-yz-xz的值](/uploads/image/z/2470011-51-1.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9Ax-y%3D5%2Cz-y%3D3%2C%E6%B1%82x%5E2%2By%5E2%2Bz%5E2-xy-yz-xz%E7%9A%84%E5%80%BC)
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已知:x-y=5,z-y=3,求x^2+y^2+z^2-xy-yz-xz的值
已知:x-y=5,z-y=3,求x^2+y^2+z^2-xy-yz-xz的值
已知:x-y=5,z-y=3,求x^2+y^2+z^2-xy-yz-xz的值
x-y=5,z-y=3
两式想减得
x-z=2
x^2+y^2+z^2-xy-yz-xz
=1/2(2x^2+2y^2+2z^2-2xy-2yz-2xz)
=1/2(x-y)²+1/2(z-y)²+1/2(x-z)²
=1/2(25+9+4)
=19
所求式子可以转化成((x-y)^2+(y-z)^2+(z-x)^2)/2-3/2
由已知可知,x-y=5
z-y=3
x-z=2
代入得(5^2+3^2+2^2)/2-3/2=35/2
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