实数x,y,z,若x2+y2=1,y2+z2=2,z2+x2=2,则xy+yz+zx的最小值是 怎求

x2+y2=1,
y2+z2=2,
z2+x2=2
三式相加,可得
x²+y²+z²=(1+2+2)/2=5
x²+y²+z²+(xy+yz+zx)
=(1/2)[(x+y)²+(y+z)²+(z+x)²]>=0
xy+yz+zx>=-(x²+y²+z²)=-5/2
xy+yz+zx>=-5/2
xy+yz+zx的最小值是-5/2