Question

已知X-Y=2,Y-Z=1,试求X2+Y2+Z2-XY-YZ-ZX

Answer 1

由x-y=2,y-z=1

两式相加,得

x-z=3

所以

x^2+y^2+z^2-xy-yz-zx

=(2x^2+2y^2+2z^2-2xy-2yz-2zx)/2

=[(x^2+y^2-2xy)+(x^2+z^2-2zx)+(y^2+z^2-2zy)]/2

=[(x-y)^2+(x-z)^2+(y-z)^2]/2

=[2^2+1^2+3^2]/2

=7