已知x+15=y+12=z+5,求x^2+y^2+z^2-xy-xz-yz

题目

已知x+15=y+12=z+5,求x^2+y^2+z^2-xy-xz-yz
今晚要

答案

x^2+y^2+z^2-xy-xz-yz
=1/2(2x^2+2y^2+2z^2-2xy-2xz-2yz)
=1/2[(x-y)^2+(x-z)^2+(y-z)^2]
=1/2[(12-15)^2+(5-15)^2+(5-12)^2]
=1/2(9+100+49)
=79