问道题吧!急!~~
来源:百度知道 编辑:UC知道 时间:2024/08/22 01:29:43
(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
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