已知x-y=(1+√3)/2,z-y=(1-√3)/2,求x²+y²+z²-xy-yz-xz的值.RT,我解不出来了.

Question

已知x-y=(1+√3)/2,z-y=(1-√3)/2,求x²+y²+z²-xy-yz-xz的值.
RT,我解不出来了.

Answer 1

x-y=(1+√3)/2 .(1)
z-y=(1-√3)/2 .(2)
(1)-(2)：(x-z)=√3 .（3）
(1)²+(2)²+(3)²得：
(x-y)²+(z-y)²+(x-z)² = [(1+√3)/2]²+[(1-√3)/2)]²+[√3]²
2x²+2y²+2z²-2xy-2yz-2xz = 5
x²+y²+z²-xy-yz-xz = 5/2