x+y+z=1 1/x+1/y+1/z=1得 xy+yz+zx=xyz 2xy+2yz+2zx=2xyz xy+yz+yz+zx+xy+zx= y(1-y)+z(1-z)+x(1-x)=2xyz x+y+z-x^2-y^2-z^2=2xyz x^2+y^2+z^2+2xyz-1=0 (x-1)(y-1)(z-1)=0 x,y,z中至少一个为1
