若x-y=m,y-z=n,试求x²+y²+z²-xy-yz-xz的值
问题描述：
若x-y=m,y-z=n,试求x²+y²+z²-xy-yz-xz的值
答
x-y=m
y-z=n
相加
x-z=m+n
原式=(2x²+2y²+2z²-2xy-2yz-2xz)/2
=[(x²-2xy+y²)+(y²-2yz+z²)+(z²-2xz+x²)]/2
=[(x-y)²+(y-z)²+(x-z)²]/2
=(m²+n²+m²+2mn+n²)/2
=m²+mn+n²