若a+b+c/d=a+b+d/c=a+c+d/b=a+c+d/a=k
问题描述：
若a+b+c/d=a+b+d/c=a+c+d/b=a+c+d/a=k
1）k=?
2)a+b+c+d/a+b+c-d=?
答
取倒数因为a/(b+c+d)=b/(a+c+d)所以{a/(b+c+d)} +1 = {b/(a+c+d)} +1 所以{a/(b+c+d)} + {(b+c+d)/(b+c+d)} = {b/(a+c+d)} + {(a+c+d)/(a+c+d)} 所以 (a+b+c+d)/(b+c+d) = (a+b+c+d) / (a+c+d)所以 (b+c+d)*(a+b+c+d...那第二小题呢？等一下(a+b+c)/d=k推出a+b+c=dk同理a+b+d=ck,a+c+d=bk,b+c+d=ak四式相加，3(a+b+c+d)=k(a+b+c+d)所以，得：k=3或a+b+c+d=0,即k=-1当k=3时，a+b+c=3d,原式=2当k=-1时,原式=0