Question

已知a/x=bc/(b+c),b/y=ca/(c+a),c/z=ab/(a+b),试求1/(x+1)+1/(y+1)+1

Answer 1

x=a(b+c)/(bc),y=b(c+a)/(ca),z=c(a+b)/(ab)

x+1=(ab+ca+bc)/(bc),y+1=(bc+ba+ca)/(ca),z+1=(ca+cb+ab)/(ab)

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