简便计算:(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)

来源:学生作业帮助网 编辑:作业帮 时间:2022/10/04 20:58:15
简便计算:(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)

简便计算:(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)
简便计算:(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)

简便计算:(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)
原式=(1+1/11+1/13+1/17)*(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17)*(1/11+1/13+1/17)-1/19*(1/11+1/13+1/17)
=(1+1/11+1/13+1/17)*1/19-1/19*(1/11+1/13+1/17)
=1/19*1
=1/19

令a=1/11+1/13+1/17
原式=(1+a)(a+1/19)-(1+a+1/19)a
=(1+a)a+1/19(1+a)-(1+a)a-1/19a
=1/19(1+a)-1/19a
=1/19+1/19a-1/19a
=1/19

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

令a=1/11+1/13+1/17,b=1/11+1/13+1/17+1/19,
类似于(1+a)*b-(1+b)*a=b+ab-a-ab=b-a=1/19

替代法:令1/11+1/13+1/17=m;1/11+1/13+1/17+1/19=n
原式(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)=(m+1)×n—(n+1)×m
=mn+n-mn-m
=n-m
=(1/11+1/13+1/17+1/19)—(1/11+1/13+1/17)
=1/19