x+y+z=1,且x/1+y/1+z/1=0,求x,y,z的平方和.用初一的知识

Question

x+y+z=1,且x/1+y/1+z/1=0,求x,y,z的平方和.
用初一的知识

Answer 1

1/x+1/y+1/z
=(yz+xz+xy)/xyz=0
yz+xz+xy=0
x^2+y^2+z^2
=(x+y+z)^2-2(xy+yz+zx)
=1^2-0
=1