已知x-y=y-z=3/5,x²+y²+z²=1.求xy+yz+zx的值
问题描述：
已知x-y=y-z=3/5,x²+y²+z²=1.求xy+yz+zx的值
答
x-y=y-z=3/5 x-z=6/5
(x-y)^2+(y-z)^2+(x-z)^2=x^2+y^2-2xy+y^2+z^2-2yz+x^2+z^2-2xz
=2(x^2+y^2+z^2)-2(xy+yz+xz)=2*1-2(xy+yz+xz)
=54/25
xy+yz+xz=-2/25