设x=by+cz,y=cz+ax,z=ax+by,求(a/a+1)+(b/b+1)+(c/c+1)的值

题目

设x=by+cz,y=cz+ax,z=ax+by,求(a/a+1)+(b/b+1)+(c/c+1)的值

答案

x=by+cz
ax=y-cz
=>(a+1)x=(b+1)y
同理可有
(c+1)z=(b+1)y
(a+1)x=(c+1)z
原式=ax/(b+1)y + by/(b+1)y + cz/(b+1)y
=(ax+by+cz)/(b+1)y
=(z+cz)/(b+1)y
=1