Question

已知x-y=5,y-z=4,求xx+yy+zz-xy-yz-xz的值

Answer 1

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