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