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速算题求救(1/10+1/11+1/12+1/13)乘以(1/11+1/12+1/13+1/14)减(1/10+1/11+1/12+1/13+1/14)乘以(1/11+1/12+1/13)
题目详情
速算题 求救
(1/10+1/11+1/12+1/13)乘以(1/11+1/12+1/13+1/14) 减(
1/10+1/11+1/12+1/13+1/14)乘以(1/11+1/12+1/13)
(1/10+1/11+1/12+1/13)乘以(1/11+1/12+1/13+1/14) 减(
1/10+1/11+1/12+1/13+1/14)乘以(1/11+1/12+1/13)
▼优质解答
答案和解析
设(1/10+1/11+1/12+1/13)*(1/11+1/12+1/13）=a
则：(1/10+1/11+1/12+1/13)*(1/11+1/12+1/13+1/14)-(
1/10+1/11+1/12+1/13+1/14)*(1/11+1/12+1/13)
=(1/14)(1/10+1/11+1/12+1/13)+a-[(1/14)(1/11+1/12+1/13)+a]
=(1/14)(1/10+1/11+1/12+1/13)-(1/14)(1/11+1/12+1/13)
再设1/14)(1/11+1/12+1/13)=b
则：=(1/14)(1/10+1/11+1/12+1/13)-(1/14)(1/11+1/12+1/13)
=(1/14)(1/10)+b-b
=1/140
则：(1/10+1/11+1/12+1/13)*(1/11+1/12+1/13+1/14)-(
1/10+1/11+1/12+1/13+1/14)*(1/11+1/12+1/13)
=(1/14)(1/10+1/11+1/12+1/13)+a-[(1/14)(1/11+1/12+1/13)+a]
=(1/14)(1/10+1/11+1/12+1/13)-(1/14)(1/11+1/12+1/13)
再设1/14)(1/11+1/12+1/13)=b
则：=(1/14)(1/10+1/11+1/12+1/13)-(1/14)(1/11+1/12+1/13)
=(1/14)(1/10)+b-b
=1/140
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