13问答网 > 求答案(1+1⼀2002+1⼀2003+1⼀2004)*(1⼀2002+1⼀2003+1⼀2004+1⼀2005)-(1+1⼀2002+1⼀2003+1⼀2004+1⼀2005)*(1⼀20

求答案(1+1⼀2002+1⼀2003+1⼀2004)(1⼀2002+1⼀2003+1⼀2004+1⼀2005)-(1+1⼀2002+1⼀2003+1⼀2004+1⼀2005)(1⼀20

2025-02-28 13:52:55

推荐回答（4个）

回答1：

令1+1/2002+1/2003+1/2004=a，1+1/2002+1/2003+1/2004+1/2005=b
原式=a×（b-1）-b（a-1）
=ab-a-ab＋b
=b-a
=1/2005

回答2：

令a=1/2002+1/2003+1/2004
则原式=(1+a)(a+1/2005)-(1+a+1/2005)a
=(1+a)a+1/2005(1+a)-(1+a)a-1/2005a
=1/2005(1+a)-1/2005a
=1/2005+1/2005a-1/2005a
=1/2005

回答3：

let

x=1/2002+1/2003+1/2004

(1+1/2002+1/2003+1/2004)*(1/2002+1/2003+1/2004+1/2005)-(1+1/2002+1/2003+1/2004+1/2005)*(1/2002+1/2003+1/2004)
=(1+x)*(x+1/2005)-(1+x+1/2005)*(x)
= (1+x)x + (1+x)/2005 - (1+x)x - x/2005
=1/2005

回答4：

1+a)(a+1/2005)-(1+a+1/2005)a
=(1+a)a+1/2005(1+a)-(1+a)a-1/2005a
=1/2005(1+a)-1/2005a
=1/2005+1/2005a-1/2005a
=1/2005