x²+y²+z²-xy-xz-yz怎么做?

题目

x²+y²+z²-xy-xz-yz怎么做?

答案

x-y=2-√3
y-z=2+√3
相加
x-z=4
x²+y²+z²-xy-yz-xz
=(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
=(7-4√3+7+4√3+16)/2
=15