当x=by+cz①,y=cz+ax②,z=ax+by③时, 　　①-②得x-y=by-ax=z-ax-ax=z-2ax,得出a=(y+z-x)/2x, 　　①-③得x-z=cz-ax=cz-(y-cz)=2cz-y,得出c=(x+y-z)/2z, 　　②-③得y-z=cz-by=x-by-by=x-2by,得出b=x-y+z/2y, 　　由上得出1+a=x+y+z/2x 　　1+b=x+y+z/2y 　　1+c=x+y+z/2z 　　则1/(1+a)=2x/(x+y+z) 　　1/(1+b)=2y/(x+y+z) 　　1/(1+c)=2z/(x+y+z) 　　则a/(a+1)+b/(b+1)+c/(c+1)==｛(y+z-x)/2x｝*｛2x/(x+y+z)｝+ 　　｛(x-y+z)/2y｝*｛2y(x+y+z)｝+｛(x+y-z)/2z｝*｛2z/(x+y+z)｝ 　　=(y+z-x+x-y+z+x+y-z)/(x+y+z)=1