已知a/b=c-d(b加减d不等于0)，求证(a+c)/(a-c)=(b+d)/(b-d)

显示全部楼层 · 2010-9-29 12:06:19

a/b=c-d？应该是a/b=c/d则a/c=b/dk=a/c=b/da=ck,b=dk所以(a+c)/(a-c)=(ck+c)/(ck-c)=c(k+1)/c(k-1)=(k+1)/(k-1)(b+d)/(b-d)=(dk+d)/(dk-d)=d(k+1)/d(k-1)=(k+1)/(k-1)所以(a+c)/(a-c)=(b+d)/(b-d)

千问 · 2010-9-29 12:06:19

解：设a/b=c/d =k那么a=kb，c=kd∴(a+c)/(b+d）=（kb+kd）/(b+d)=k(b+d)/(b+d)=k(a-c)/(b-d)=(kb-kd)/(b-d)=k(b-d)/(b-d)=k∴(a+c)/(b+d)=(a-c)/(b-d)∴(a+c)/(a-c)=(b+d)/(b-d)a/b=c/d

千问 · 2010-9-29 12:06:19

由已知 a/b=c/d 可得 ad=bc 2ad=2bc =