已知x-y=5,z-y=10,X^2+Y^2+Z^2-XY-YZ-ZX

来源：学生作业帮助网编辑：作业帮时间：2024/11/17 16:19:17

已知x-y=5,z-y=10,X^2+Y^2+Z^2-XY-YZ-ZX
已知x-y=5,z-y=10,X^2+Y^2+Z^2-XY-YZ-ZX

已知x-y=5,z-y=10,X^2+Y^2+Z^2-XY-YZ-ZX
x-y=5,z-y=10
相减
z-x=5
x²+y²+z²-xy-yz-xz
=(2x²+2y²+2z²-2xy-2yz-2xz)/2
=[(x²-2xy+y²)+(y²-2yz+z²)+(z²-2xz+x²)]/2
=[(x-y)²+(y-z)²+(z-x)²]/2
=(25+100+25)/2
=75

这道题可以用拼凑法
（x-y）²+（z-y）²=x²+z²+2y²-2xy-2yz
（x-y）²+（z-y）²-y²+xy+yz-xz=25+100-y(y-z)+x(y-z)
所以得到结果75

=(2x²+2y²+2z²-2xy-2yz-2xz)/2
=[(x²-2xy+y²)+(y²-2yz+z²)+(z²-2xz+x²)]/2
=[(x-y)²+(y-z)²+(z-x)²]/2
=(25+100+25)/2
=75

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