问道题吧！急！~~

来源：百度知道 编辑：UC知道 时间：2024/06/21 01:54:26
（1+1/11+1/13+1/17）*(1/11+1/13+1/17+1/19)*(1+1/11+1/13+1/17+1/19)*(1/11+1/13+1/17)

用简便的算法！！~帮忙……谢谢
能不能再详细点？~
MS有点……答案，好像……是19

写错了吧
应该是(1+1/11+1/13+1/17)*(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17+1/19)*(1/11+1/13+1/17)
令a=1/11+1/13+1/17
则原式=(1+a)(a+1/19)-(1+a+1/19)*a
=(1+a)*a+(1+a)*(1/19)-(1+a)*a-a*(1/19)
=(1+a)*(1/19)-a*(1/19)
=(1+a-a)*(1/19)
=1/19

解：令
1/11+1/13+1/17=A

1/11+1/13+1/17+1/19=B

原式=(1+A)×B-(1+B)*A

=B+A×B-A-A×B

=B-A

=1/19

（1+1/11+1/13+1/17）*(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17+1/19)*(1/11+1/13+1/17)
=(1+1/11+1/13+1/17)*(1/11+1/13+1/17+1/19)-(1/11+1/13+1/17+1/19)(1/11+1/13+1/17)-(1/11+1/13+1/17)
=(1/11+1/13+1/17+1/19)-(1/11+1/13+1/17)
=1/19