设x=by+cz,y=cz+ax,z=ax+by,求(a/a+1)+(b/b+1)+(c/c+1)的值
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![设x=by+cz,y=cz+ax,z=ax+by,求(a/a+1)+(b/b+1)+(c/c+1)的值](/uploads/image/z/6787069-61-9.jpg?t=%E8%AE%BEx%3Dby%2Bcz%2Cy%3Dcz%2Bax%2Cz%3Dax%2Bby%2C%E6%B1%82%28a%2Fa%2B1%29%2B%28b%2Fb%2B1%29%2B%28c%2Fc%2B1%29%E7%9A%84%E5%80%BC)
设x=by+cz,y=cz+ax,z=ax+by,求(a/a+1)+(b/b+1)+(c/c+1)的值
设x=by+cz,y=cz+ax,z=ax+by,求(a/a+1)+(b/b+1)+(c/c+1)的值
设x=by+cz,y=cz+ax,z=ax+by,求(a/a+1)+(b/b+1)+(c/c+1)的值
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