Question

x(1/y+1/z)+y(1/x+1/z)+z(1/x+1/y)+3=0,且1/x+1/y+1/z不等于0,求x+y+z

Answer 1

把3拆成1+1+1

x/y+x/z+y/x+y/z+z/x+z/y+1+1+1=0

(x/y+z/y+1)+(z/x+y/x+1)+(x/z+y/z+1)=0

(x+y+z)/y+(x+y+z)/x+(x+y+z)/z=0

(x+y+z)(1/x+1/y+1/z)=0

1/x+1/y+1/z不等于0,

所以x+y+z=0