已知x-y=5,y-z=4,求xx+yy+zz-xy-yz-xz的值

x-z=(x-y)+(y-z)=5+4=9
(x-y)²=x²-2xy+y²=25
(y-z)²=y²-2yz+z²=16
(x-z)²=x²-2xz+z²=81
上面的三个式子相加得
x²-2xy+y²+y²-2yz+z²+x²-2xz+z²=25+16+81
2(xx+yy+zz-xy-yz-xz)=122
xx+yy+zz-xy-yz-xz=61