已知x+y+z=1,且xy+yz+zx=0,求x²+y²+z²的值.
问题描述:
已知x+y+z=1,且xy+yz+zx=0,求x²+y²+z²的值.
答
(x+Y+Z)^2=x^2+2XY+Y^2+2YZ+Z^2+2ZX
X^2+Y^2+Z^2=(X+Y+Z)^2-2(XY+YZ+ZX)=1-0=1