Question

一道简单的数学题若X-Y=M,Y-Z=N,则X^2+Y^2+Z^2-XY-YZ-ZX的值为( )M^2+N^2+MN 求

Answer 1

X^2+Y^2+Z^2-XY-YZ-ZX

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

而

x-z=M+N

所以

X^2+Y^2+Z^2-XY-YZ-ZX

=(2M^2+2N^2+2MN)/2

=M^2+N^2+MN