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(1/5+1/7+1/9+14/11)*(1/7+1/9+1/11+1/13)-(1/5+1/7+1/9+1/11+1/13)*(1/7*1/9+1/11)=?记得要写分析、过程!
题目详情
(1/5+1/7+1/9+14/11)*(1/7+1/9+1/11+1/13)-(1/5+1/7+1/9+1/11+1/13)*(1/7*1/9+1/11)=?
记得要写分析、过程!
记得要写分析、过程!
▼优质解答
答案和解析
【题目打错了呵呵,第一个括号里面应该是1/5+1/7+1/9+1/11,而不是1/5+1/7+1/9+14/11;第四个括号里面应该是1/7+1/9+1/11,而不是1/7*1/9+1/11】
(1/5+1/7+1/9+1/11)*(1/7+1/9+1/11+1/13)-(1/5+1/7+1/9+1/11+1/13)*(1/7*1/9+1/11)
设1/5+1/7+1/9+1/11=A,1/7+1/9+1/11=B,则
原式=A×(B+1/13)-(A+1/13)×B
=AB+1/13A-AB-1/13B
=1/13(A-B)
=1/13×1/5
=1/65
(1/5+1/7+1/9+1/11)*(1/7+1/9+1/11+1/13)-(1/5+1/7+1/9+1/11+1/13)*(1/7*1/9+1/11)
设1/5+1/7+1/9+1/11=A,1/7+1/9+1/11=B,则
原式=A×(B+1/13)-(A+1/13)×B
=AB+1/13A-AB-1/13B
=1/13(A-B)
=1/13×1/5
=1/65
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