已知1/x+1/y+1/z=0,x²+y²+z²=4求x+y+z

已知1/x+1/y+1/z=0,x²+y²+z²=4求x+y+z
已知1/x+1/y+1/z=0,x²+y²+z²=4求x+y+z

已知1/x+1/y+1/z=0,x²+y²+z²=4求x+y+z
1/x+1/y+1/z=0
通分
(yz+xz+xy)/xyz=0
∵xyz≠0
∴yz+xz+xy=0
(x+y+z)^2
=x^2+y^2+z^2+2(xy+xz+yz)
=4+2*0
=4
∴x+y+z=2或-2

1/x+1/y+1/z=0
(xy+xz+yz)/xyz=0
xy+xz+yz=0
2xy+2xz+2yz=0
(x+y+z)²=x²+2xy+2xz+2yz+y²+z²=4
x+y+z=-2
x²+y²+z²=4求x+y+z

1/x+1/y+1/z=0=>xy+xz+yz=0①；x^2+y^2+z^2=4②；①*2+②=（x+y+z）^2=4;所以x+y+z=2or-2