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