已知x(1/y+1/x)+y(1/x+1/z)+z(1/x+1/y)+3=0,且1/x+1/y+1/z不等于零,求x+y+z的值
问题描述:
已知x(1/y+1/x)+y(1/x+1/z)+z(1/x+1/y)+3=0,且1/x+1/y+1/z不等于零,求x+y+z的值
答
把3拆成1+1+1x/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)=01/x+1/y+1/z不等于0,所以x+y+z=0