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(l-1/2-1/3-1/4-1/5)(1/2+1/3+1/4+1/5+1/6)一(l-1/2-/3-1/4-1/5-1/6)(1/2+1/3+1/4+1/5)怎么算
题目详情
(l-1/2-1/3-1/4-1/5)(1/2+1/3+1/4+1/5+1/6)一(l-1/2-
/3-1/4-1/5-1/6)(1/2+1/3+1/4+1/5)怎么算
/3-1/4-1/5-1/6)(1/2+1/3+1/4+1/5)怎么算
▼优质解答
答案和解析
答：
设a=1/2+1/3+1/4+1/5+1/6
原式
=(l-1/2-1/3-1/4-1/5)(1/2+1/3+1/4+1/5+1/6)一(l-1/2-1/3-1/4-1/5-1/6)(1/2+1/3+1/4+1/5)
=[1-(a-1/6)]*a-(1-a)(a-1/6)
=(7/6-a)a+(a-1)(a-1/6)
=7a/6-a^2+a^2-7a/6+1/6
=1/6
设a=1/2+1/3+1/4+1/5+1/6
原式
=(l-1/2-1/3-1/4-1/5)(1/2+1/3+1/4+1/5+1/6)一(l-1/2-1/3-1/4-1/5-1/6)(1/2+1/3+1/4+1/5)
=[1-(a-1/6)]*a-(1-a)(a-1/6)
=(7/6-a)a+(a-1)(a-1/6)
=7a/6-a^2+a^2-7a/6+1/6
=1/6
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