Question

已知x-y=(1+√3)/2,z-y=(1-√3)/2,求x²+y²+z²-xy-yz-x

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